Scalar list: Physics Derivation Graph

There are 221 Scalars, aka symbols of dimension 0

The symbol ID links to a page where you can edit the symbol

Case-insensitive fuzzy Search:

ID	latex	name	description	scope	domain	used in expression	used in derivation	variable or constant	reference	dimension: time	dimension: length	dimension: mass	dimension: electric charge	dimension: amount of substance	dimension: temperature
0000001054	\(\hbar\) \hbar	Reduced Planck's constant		real	any	1648958381 1556389363 1158485859 9999999965 9999999962 9999999961 9999999960 9999999870 9999998870 9958485859 9640720571 8106885760 5985371230 5868688585 5838268428 4943571230 4394958389 4348571256 4341171256 3948574233 3948574230 3948574228 3948574226 3948571256 3935058307 3291685884 2395958385 2258485859 2648958382	derivation of Schrodinger Equation upper limit on velocity in condensed matter	constant	https://en.wikipedia.org/wiki/Planck_constant#Value	-1	2	1	0	0	0
0000001088	\(W\) W	work done to a system		real	any	1815398659	first law of thermodynamics	variable	https://en.wikipedia.org/wiki/Work_(thermodynamics)	-2	2	1	0	0	0
0000001115	\(\lambda\) \lambda	wavelength		real	any	1293923844 1020394900 0404050504 3121513111 3121234211	derivation of Schrodinger Equation frequency relations	variable	https://en.wikipedia.org/wiki/Wavelength	0	1	0	0	0	0
0000001134	\(p\) p	momentum		real	any	1029039904 1029039903 1020394900 9999999962 9999999870 5868688585 4348571256 4341171256 4298359851 3948574233 3948574230 3948574228 3948574226 2395958385 3121234212	derivation of Schrodinger Equation	variable	https://en.wikipedia.org/wiki/Momentum	-1	1	1	0	0	0
0000001157	\(k_{\rm Boltzmann}\) k_{\rm Boltzmann}	Boltzmann constant		real	any	3547519267	first law of thermodynamics	constant	https://en.wikipedia.org/wiki/Boltzmann_constant	-2	2	1	0	0	-1
0000001352	\(KE_2\) KE_2	kinetic energy		real	any	9356924046 7875206161 7735737409 7676652285 5733146966 5514556106 4784793837 4270680309 3591237106 3360172339 2186083170 2770069250	time invariant force conserves energy escape velocity work and force and energy	variable	https://en.wikipedia.org/wiki/Kinetic_energy	-2	2	1	0	0	0
0000001356	\(k\) k	linear stiffness, aka spring constant		real	any	1931103031 1888494137 1784114349 8991236357 8655294002 4428528271 2334518266	equation of motion for a spring	variable	https://en.wikipedia.org/wiki/Stiffness	-2	0	1	0	0	0
0000001357	\(v\) v	velocity		real	any	9226945488 1967582749 1935543849 1916173354 1639827492 1586866563 1528310784 1293923844 1259826355 1029039904 1029039903 0934990943 0404050504 9897284307 9805063945 9759901995 9397152918 9337785146 1974334644 2005061870 2542420160 2096918413 2186083170 2924222857 2983053062 2999795755 2417941373 3182633789 3214170322 3366703541 3426941928 3462972452 3591237106 3614055652 4139999399 4245712581 4267808354 4298359835 4298359845 4580545876 4662369843 4748157455 4784793837 4798787814 4872970974 4948763856 5144263777 5177311762 5426308937 5611024898 5733721198 5763749235 5900595848 6175547907 6421241247 6457044853 6946088325 7215099603 7513513483 7735737409 7741202861 7939765107 8059639673 8269198922 8357234146 8360117126 8361238989 8706092970	derivation of Schrodinger Equation frequency relations time invariant force conserves energy escape velocity Newton's Law of Gravitation radius for satellite in geostationary orbit equations of motion in 1D with constant acceleration - SUVAT (algebra) velocity at distance r of object dropped from infinity speed of Earth around Sun Lorentz transformation work and force and energy	variable	https://en.wikipedia.org/wiki/Velocity	-1	1	0	0	0	0
0000001370	\(\alpha\) \alpha	fine-structure constant		real	any	8106885760 7701249282 5838268428 5789289057 2897612567	upper limit on velocity in condensed matter	constant	https://en.wikipedia.org/wiki/Fine-structure_constant	0	0	0	0	0	0
0000001394	\(S\) S	entropy		real	any	3547519267	first law of thermodynamics	variable	https://en.wikipedia.org/wiki/Entropy	-2	2	1	0	0	-1
0000001434	\(\hat{x}_n\) \hat{x}_n	nth unit vector		real	any	7575859310	curl curl identity	variable		0	0	0	0	0	0
0000001452	\(y\) y			real	any	9848294829 9848292229 9492920340 9482984922 9482943948 9482923849 9429829482 5781981178 4928239482 4923339482	time invariant force conserves energy Euler equation proof	variable		0	0	0	0	0	0
0000001464	\(x\) x			real	any	5959282914 7764834870 8637447837 9605409442 1934748140 1395858355 1248277773 1128605625 1038566242 1010393944 0948572140 0203024440 9999999969 9999999968 9988949211 9894826550 9889984281 9858028950 9848294829 9596004948 9585727710 9582958294 9582958293 9492920340 9483928192 9482984922 9482928243 9482928242 9482923849 9482438243 9429829482 9413609246 9393939992 9393939991 9385938295 9285928292 9180861128 9059289981 8889444440 8747785338 8699789241 8651044341 8588429722 8582954722 8576785890 8575748999 8575746378 8572657110 8563535636 8532702080 8483686863 8418527415 8399484849 7735731560 7731226616 7575738420 6404535647 6031385191 5982958249 5982958248 2494533900 2700934933 2103023049 2121790783 2123139121 2762326680 2902772962 2944838499 2394240499 2394853829 2404934990 2405307372 3285732911 3470587782 3585845894 3660957533 3676159007 3829492824 3868998312 3942849294 4166155526 4585932229 4598294821 4638429483 4662369843 4742644828 4805233006 4827492911 4830221561 4838429483 4843995999 4872163189 4878728014 4923339482 4928239482 4938429482 4938429483 4938429484 4949359835 4968680693 5323719091 5349669879 5781981178 5832984291 5857434758 5866629429 5928285821 5928292841 5938459282 5958392859	Euler's equation from MacLaurin series particle in a 1D box quadratic equation derivation quantum basics orthogonality variance relation identity sin(2 x) = 2 sin(x) cos(x) using Euler's equation Euler equation to exp(i pi) + 1 = 0 time invariant force conserves energy equations of motion in 2D (calculus) angle of maximum distance for projectile motion optics: Law of refraction to Brewster's angle double intensity when phase is coherent (optics) Lorentz transformation hyperbolic trigonometric identities Euler equation proof Euler equation: trig square root Euler equation: trigonometric relations	variable		0	0	0	0	0	0
0000001466	\(K\) K	bulk modulus		real	any	4560648264	upper limit on velocity in condensed matter	variable	https://en.wikipedia.org/wiki/Bulk_modulus	-2	-1	1	0	0	0
0000001467	\(t\) t	time		real	any	5985371230 1967582749 1935543849 1858578388 1819663717 1809909100 1772416655 1648958381 1586866563 1405465835 1314864131 1314464131 1306360899 1265150401 1259826355 9991999979 9973952056 9958485859 9897284307 9882526611 9862900242 9805063945 9759901995 9658195023 9499428242 9485384858 9394939493 9356924046 9337785146 9291999979 8808860551 8750379055 8706092970 8572852424 8494839423 8486706976 8460820419 8228733125 8145337879 7741202861 7735737409 7729413831 7652131521 7455581657 7267155233 7252338326 7215099603 7011114072 6946088325 6908055431 6572039835 6457044853 6421241247 6204539227 1974334644 1977955751 2461349007 2029293929 2096918413 2770069250 2186083170 2857430695 2858549874 2258485859 2366691988 2395958385 3169580383 3274926090 3366703541 3411994811 3426941928 3462972452 3591237106 3676159007 3947269979 3948571256 3948574224 3948574226 3948574228 3948574230 3948574233 4139999399 4158986868 4245712581 4270680309 4287102261 4341171256 4348571256 4370074654 4394958389 4580545876 4662369843 4748157455 4784793837 4798787814 4872970974 4943571230 4985825552 5373931751 5415824175 5426308937 5438722682 5868688585 5945893986	derivation of Schrodinger Equation electric field wave equation: from time dependent to time independent time invariant force conserves energy equations of motion in 2D (calculus) angle of maximum distance for projectile motion Newton's Law of Gravitation radius for satellite in geostationary orbit equations of motion in 1D with constant acceleration - SUVAT (algebra) speed of Earth around Sun Lorentz transformation equation of motion for a spring projectile path in 2D is parabolic Maxwell equations to electric field wave equation	variable	https://en.wikipedia.org/wiki/Time_in_physics	1	0	0	0	0	0
0000001469	\(y_0\) y_0	initial position		real	any	1650441634 1405465835 9862900242 8198310977 7354529102 5379546684 2858549874 2461349007	equations of motion in 2D (calculus) angle of maximum distance for projectile motion projectile path in 2D is parabolic	variable		0	1	0	0	0	0
0000001534	\(C_{\rm Earth\ orbit}\) C_{\rm Earth\ orbit}	circumference of Earth's orbit		real	any	6348260313 3046191961	speed of Earth around Sun	variable	https://en.wikipedia.org/wiki/Earth%27s_orbit	0	1	0	0	0	0
0000001552	\(j\) j	index		integer	any	1840080113 8960645192 7575859308 7575859306 7575859304 7575859302 7575859300	curl curl identity escape velocity	variable		0	0	0	0	0	0
0000001567	\(i\) i	index		integer	any	7575859302	curl curl identity	variable		0	0	0	0	0	0
0000001572	\(x_0\) x_0	initial position		real	any	1306360899 9882526611 8486706976 7354529102 5438722682 4268085801 3485125659 3274926090 2378095808	equations of motion in 2D (calculus) angle of maximum distance for projectile motion projectile path in 2D is parabolic	variable		0	1	0	0	0	0
0000001575	\(\theta\) \theta	angle		real	any	1541916015 1357848476 1191796961 1087417579 9862900242 8949329361 8922441655 8602221482 8497631728 8198310977 7621705408 7391837535 7376526845 7233558441 6774684564 6555185548 6083821265 5438722682 5379546684 4778077984 4268085801 4182362050 3660957533 3485125659 3085575328 2297105551 2086924031 2700934933 2519058903	equations of motion in 2D (calculus) angle of maximum distance for projectile motion double intensity when phase is coherent (optics)	variable	https://en.wikipedia.org/wiki/Angle	0	0	0	0	0	0
0000001592	\(n\) n	index		integer	any	8637447837 7764834870 1858772113 1857710291 1202312210 1202310110 1010923823 0439492440 0203024440 9858028950 9393939992 9393939991 8889444440 8849289982 8576785890 7575859310 7575859308 7575859306 7575859304 7575859302 7575738420 7564894985 2944838499	curl curl identity Euler's equation from MacLaurin series particle in a 1D box	variable		0	0	0	0	0	0
0000001649	\(g\) g	acceleration due to gravity		real	any	1702349646 1405465835 1191796961 1087417579 9973952056 9862900242 8922441655 8808860551 8198310977 8145337879 7354529102 6572039835 5379546684 5353282496 4778077984 3607070319 2297105551 2858549874 2741489181 2086924031 2484824786 1977955751 2461349007	equations of motion in 2D (calculus) angle of maximum distance for projectile motion mass of the Earth projectile path in 2D is parabolic	variable	https://en.wikipedia.org/wiki/Gravity	-2	1	0	0	0	0
0000001687	\(F_{\rm centripetal}\) F_{\rm centripetal}	centripetal force		real	any	6829281943 6026694087 4820320578 4627284246 4393258808 3649797559 3176662571	Newton's Law of Gravitation radius for satellite in geostationary orbit Kepler's Third Law: period squared propto distance cubed	variable	https://en.wikipedia.org/wiki/Centripetal_force	-2	1	1	0	0	0
0000001700	\(\hat{y}\) \hat{y}	unit vector		real	any	9341391925 8602512487 7729413831 5349866551	equations of motion in 2D (calculus)	variable	https://en.wikipedia.org/wiki/Unit_vector	0	0	0	0	0	0
0000001790	\(\gamma\) \gamma	Lorentz factor		real	any	1935543849 1916173354 1639827492 1586866563 1528310784 9805063945 9409776983 9031609275 8730201316 8360117126 7906112355 7741202861 7513513483 5763749235 5148266645 4662369843 4139999399 3426941928 3182633789 2417941373 2999795755 2983053062 2096918413 2076171250 2542420160 1974334644	Lorentz transformation	variable	https://en.wikipedia.org/wiki/Lorentz_factor	0	0	0	0	0	0
0000001791	\(\theta_A\) \theta_A	the fraction of the surface sites covered with A		real	any	8131665171 7928111771 7267424860 4689334676 2114909846	Langmuir Adsorption	variable	https://en.wikipedia.org/wiki/Langmuir_adsorption_model	0	0	0	0	0	0
0000001888	\(y'\) y'	position in moving reference frame		real	any	1201689765 7057864873	Lorentz transformation	variable	https://en.wikipedia.org/wiki/Frame_of_reference	0	1	0	0	0	0
0000001900	\(d\) d			real	any			variable		0	0	0	0	0	0
0000001908	\(R_{\rm total}\) R_{\rm total}	electrical resistance		real	any	1457415749 7217021879 4939880586 4866160902 2271186630 2809345867 2715678478	total electrical resistance for circuit with two resistors in parallel total electrical resistance for circuit with two resistors in series	variable	https://en.wikipedia.org/wiki/Electrical_resistance_and_conductance	-1	2	1	-2	0	0
0000001934	\(v_{\rm initial}\) v_{\rm initial}	initial velocity		real	any	6091977310 2998709778 2924222857	velocity at distance r of object dropped from infinity	variable	https://en.wikipedia.org/wiki/Velocity	-1	1	0	0	0	0
0000001939	\(b\) b			real	any	1293913110 9999999969 9999999968 9582958294 9582958293 9385938295 9285928292 8582885111 8577275751 8575748999 5982958249 5982958248 5959282914 5938459282 5928292841 5928285821	particle in a 1D box quadratic equation derivation	variable		0	0	0	0	0	0
0000001943	\(d\) d	displacement		real	any	1265150401 1259826355 9897284307 9658195023 9262596735 8922441655 8706092970 8269198922 7939765107 7233558441 7011114072 6421241247 5733721198 5611024898 5426308937 5353282496 4948763856 4580545876 4268085801 3607070319 3411994811 2378095808 2297105551	angle of maximum distance for projectile motion Newton's Law of Gravitation radius for satellite in geostationary orbit equations of motion in 1D with constant acceleration - SUVAT (algebra) speed of Earth around Sun work and force and energy	variable	https://en.wikipedia.org/wiki/Displacement_(geometry)	0	1	0	0	0	0
0000001955	\(KE_1\) KE_1	kinetic energy		real	any	9749777192 9356924046 8960645192 7735737409 5733146966 5514556106 4928007622 4784793837 4303372136 4270680309 3591237106 3360172339 2186083170 2770069250	time invariant force conserves energy escape velocity work and force and energy	variable	https://en.wikipedia.org/wiki/Kinetic_energy	-2	2	1	0	0	0
0000001958	\(n_2\) n_2	index of refraction for material 2		real	any	9756089533 8495187962 7696214507 6450985774 3417126140 3061811650 2768857871 2575937347	optics: Law of refraction to Brewster's angle	variable	https://en.wikipedia.org/wiki/Refractive_index	0	0	0	0	0	0
0000001966	\(r_{\rm desorption}\) r_{\rm desorption}	rate of desorption		real	any	6955192897 6783009163 3507029294	Langmuir Adsorption	variable	https://en.wikipedia.org/wiki/Langmuir_adsorption_model	-1	0	0	0	0	0
0000001999	\(e\) e	charge of an electron		real	any	1556389363 9640720571 8106885760 5838268428 3935058307 3291685884	upper limit on velocity in condensed matter	constant	https://en.wikipedia.org/wiki/Elementary_charge	0	0	0	1	0	0
0000002046	\(\vec{p}\) \vec{p}	momentum		real	any	1648958381 9999998870 5985371230 4943571230 4394958389	derivation of Schrodinger Equation	variable	https://en.wikipedia.org/wiki/Momentum	-1	1	1	0	0	0
0000002077	\(v\) v	longitudinal speed of sound in condensed matter		real	any	9854442418 9640720571 8090924099 7837519722 6504442697 5789289057 4560648264 3935058307 2897612567	upper limit on velocity in condensed matter	variable	https://en.wikipedia.org/wiki/Speed_of_sound	-1	1	0	0	0	0
0000002090	\(\| \psi_{\beta} \rangle\) \| \psi_{\beta} \rangle	ket		complex	any	1395858355 1203938249 1010393944 9596004948 2394935831 2394240499	quantum basics orthogonality	variable	https://en.wikipedia.org/wiki/Bra%E2%80%93ket_notation	0	0	0	0	0	0
0000002241	\(E\) E	bonding energy		real	any	9854442418 9376481176 8090924099 7837519722 4107032818 3291685884	upper limit on velocity in condensed matter	variable		0	0	0	0	0	0
0000002243	\(\theta_{\rm refracted}\) \theta_{\rm refracted}	refracted angle		real	any	2575937347	optics: Law of refraction to Brewster's angle	variable		0	0	0	0	0	0
0000002321	\(\omega\) \omega	angular frequency		real	any	1931103031 1888494137 1858578388 1784114349 1772973171 9999999965 9999999961 9499428242 9485384858 7652131521 5945893986 5900595848 5415824175 4985825552 4393258808 4147472132 3948574226 3948574224 3896798826 3649797559 3485475729 3147472131 3132131132 3131211131 2148049269 2029293929	derivation of Schrodinger Equation electric field wave equation: from time dependent to time independent frequency relations equation of motion for a spring Kepler's Third Law: period squared propto distance cubed	variable	https://en.wikipedia.org/wiki/Angular_frequency	-1	0	0	0	0	0
0000002380	\(\hat{x}_m\) \hat{x}_m	mth unit vector		real	any	7575859310	curl curl identity	variable		0	0	0	0	0	0
0000002427	\(a_{\alpha}\) a_{\alpha}	none		complex	any	1395858355 3943939590 2394935831	quantum basics orthogonality	variable	https://en.wikipedia.org/wiki/Quantum_mechanics	0	0	0	0	0	0
0000002435	\(I_{\rm incoherent}\) I_{\rm incoherent}	intensity of incoherent waves		real	any	6556875579 6529793063 6240206408 3060393541	double intensity when phase is coherent (optics)	variable	https://en.wikipedia.org/wiki/Intensity_(physics)	-3	0	1	0	0	0
0000002467	\(t_f\) t_f	final time		real	any	1191796961 1087417579 8198310977 7233558441 5379546684 5373931751 4778077984 4370074654 4268085801 3485125659 2086924031	angle of maximum distance for projectile motion	variable		1	0	0	0	0	0
0000002473	\(v_1\) v_1	velocity 1		real	any	9413699705 9397152918 9356924046 7735737409 5733146966 4928007622 4811121942 4648451961 4270680309 3253234559 2857430695	time invariant force conserves energy work and force and energy	variable	https://en.wikipedia.org/wiki/Velocity	-1	1	0	0	0	0
0000002515	\(m_e\) m_e	mass of electron		real	any	1556389363 9640720571 7701249282 5789289057 3935058307 3291685884 2897612567	upper limit on velocity in condensed matter	constant	https://en.wikipedia.org/wiki/Electron	0	0	1	0	0	0
0000002523	\(W\) W	width		real	any	1858772113 1202312210 1202310110 1020010291 1010923823 0439492440 0203024440 9858028950 9495857278 9485747246 9485747245 9393939992 9393939991 8889444440 8849289982 8576785890 8485867742 7575738420 7564894985 4857475848 2944838499	particle in a 1D box	variable		0	1	0	0	0	0
0000002530	\(r\) r	radius		real	any	8617866819 1189963325 1994296484 2005061870 2617541067 2061086175 2906548078 3004158505 3566149658 3614055652 3650370389 3781109867 3896798826 3906710072 4072200527 4188580242 4245712581 4267808354 4393258808 4393670960 4627284246 4858693811 5177311762 5404822208 5563580265 5586102077 5658865948 5693047217 5846639423 6026694087 6268336290 6785303857 6829281943 6892595652 7010294143 7112646057 7672365885 7882872592 8059639673 8361238989 8405272745 8946383937 9070394000 9152823411 9170048197 9226945488 9262596735 9838128064 1292735067 1811867899	escape velocity Schwarzschild radius for non-rotating black hole Newton's Law of Gravitation radius for satellite in geostationary orbit velocity at distance r of object dropped from infinity speed of Earth around Sun Kepler's Third Law: period squared propto distance cubed	variable	https://en.wikipedia.org/wiki/Radius	0	1	0	0	0	0
0000002718	\(\exp\) \exp	e		real	any	9499428242 9485384858 3948574233 3948574230 3948574228 3948574226 3948574224	derivation of Schrodinger Equation electric field wave equation: from time dependent to time independent	constant	https://en.wikipedia.org/wiki/E_(mathematical_constant)	0	0	0	0	0	0
0000002798	\(d_2\) d_2	distance		real	any	1811867899 9838128064 9170048197 9152823411 9070394000 5586102077 5128670694 4188580242 3896798826 3781109867 3649797559 2906548078 2217103163	Kepler's Third Law: period squared propto distance cubed	variable	https://en.wikipedia.org/wiki/Distance	0	1	0	0	0	0
0000002834	\(n\) n	amount of substance		real	any	1311403394 1190768176 8435841627 8368984890 5962145508 3605073197 3497828859 2613006036	coefficient of thermal expansion using the equation of state for an ideal gas coefficient of isothermal compressibility using the equation of state for an ideal gas	variable	https://en.wikipedia.org/wiki/Amount_of_substance	0	0	0	0	0	0
0000002851	\(k_{\rm Debye}\) k_{\rm Debye}	Debye wavevector		real	any			variable	https://en.wikipedia.org/wiki/Debye_model	0	0	0	0	0	0
0000002867	\(F_{\rm gravity}\) F_{\rm gravity}	force due to gravity		real	any	1292735067 7672365885 6268336290 5563580265 4820320578 4267808354 3650370389 3176662571 3004158505	Newton's Law of Gravitation radius for satellite in geostationary orbit Kepler's Third Law: period squared propto distance cubed	variable	https://en.wikipedia.org/wiki/Gravity	-2	1	1	0	0	0
0000002875	\(r_{\rm Bohr}\) r_{\rm Bohr}	Bohr radius		real	any			constant	https://en.wikipedia.org/wiki/Debye_model	0	1	0	0	0	0
0000002941	\(n_1\) n_1	index of refraction for material 1		real	any	9756089533 8495187962 7696214507 6450985774 3417126140 3061811650 2768857871 2575937347	optics: Law of refraction to Brewster's angle	variable	https://en.wikipedia.org/wiki/Refractive_index	0	0	0	0	0	0
0000002958	\(v_{0, x}\) v_{0, x}	initial velocity along x axis		real	any	1963253044 1676472948 1306360899 9882526611 9341391925 8486706976 7455581657 7391837535 7354529102 6134836751 6083821265 3676159007 3274926090	equations of motion in 2D (calculus) projectile path in 2D is parabolic	variable	https://en.wikipedia.org/wiki/Velocity	-1	1	0	0	0	0
0000003033	\(G\) G	shear modulus		real	any	4560648264	upper limit on velocity in condensed matter	variable	https://en.wikipedia.org/wiki/Shear_modulus	-2	-1	1	0	0	0
0000003034	\(C\) C	circumference		real	any	6946088325 6785303857	Newton's Law of Gravitation radius for satellite in geostationary orbit speed of Earth around Sun	variable	https://en.wikipedia.org/wiki/Circumference	0	1	0	0	0	0
0000003037	\([S_0]\) [S_0]	total number of sites		real	any	8131665171 7517073655 6457999644 4301729661 3599953931 2168306601 2114909846	Langmuir Adsorption	variable	https://en.wikipedia.org/wiki/Langmuir_adsorption_model	0	0	0	0	1	0
0000003141	\(\pi\) \pi	pi		real	any	9838128064 1858772113 1857710291 1811867899 1559688463 1556389363 1541916015 1202312210 1202310110 1010923823 0934990943 0439492440 0203024440 9999999960 9858028950 2501591100 2617541067 2906548078 2944838499 3004158505 3080027960 3121234211 3121234212 3121513111 3131211131 3132131132 3147472131 3291685884 3331824625 3607070319 3614055652 3650370389 3781109867 3906710072 3935058307 4147472132 4188580242 4245712581 4593428198 4858693811 5177311762 5658865948 5838268428 6268336290 6348260313 6785303857 6885625907 6998364753 7010294143 7564894985 7575738420 7672365885 8059639673 8106885760 8332931442 8576785890 8849289982 8889444440 9070394000 9152823411 9170048197 9262596735 9393939991 9393939992 9640720571	derivation of Schrodinger Equation frequency relations particle in a 1D box Euler equation to exp(i pi) + 1 = 0 angle of maximum distance for projectile motion Newton's Law of Gravitation radius for satellite in geostationary orbit speed of Earth around Sun upper limit on velocity in condensed matter Kepler's Third Law: period squared propto distance cubed	constant		0	0	0	0	0	0
0000003192	\(Z\) Z	none		complex	any	1928085940 9191880568 4182362050 3350830826	double intensity when phase is coherent (optics)	variable	https://farside.ph.utexas.edu/teaching/315/Waveshtml/node88.html	0	0	0	0	0	0
0000003236	\(r_{\rm Earth}\) r_{\rm Earth}	radius of Earth		real	any	1330874553 1143343287 9703482302 9440616166 9412953728 9407192813 8661803554 7846240076 7749253510 5978756813 4447113478 3846041519 2977457786 2308660627 2750380042 2042298788	escape velocity mass of the Earth	constant	https://en.wikipedia.org/wiki/Earth_radius	0	1	0	0	0	0
0000003285	\(A\) A	atomic mass		real	any	5646314683 2897612567	upper limit on velocity in condensed matter	variable	https://en.wikipedia.org/wiki/Atomic_mass	0	0	1	0	0	0
0000003410	\(h\) h	none		real	any	8582954722	quadratic equation derivation	variable		0	0	0	0	0	0
0000003434	\(\Omega\) \Omega	number of microscopic configurations (known as microstates) that are consistent with the macroscopic quantities that characterize the system		real	any	3547519267	first law of thermodynamics	variable	https://en.wikipedia.org/wiki/Microstate_(statistical_mechanics)	0	0	0	0	0	0
0000003461	\(R_2\) R_2	electrical resistance		real	any	1457415749 9243879541 7217021879 7002609475 6061695358 4866160902 2715678478	total electrical resistance for circuit with two resistors in parallel total electrical resistance for circuit with two resistors in series	variable	https://en.wikipedia.org/wiki/Electrical_resistance_and_conductance	-1	2	1	-2	0	0
0000003474	\(\epsilon\) \epsilon	Levi-Civita		real	any			variable	https://en.wikipedia.org/wiki/Levi-Civita_symbol	0	0	0	0	0	0
0000003509	\(\theta_1\) \theta_1	angle		real	any	6450985774	optics: Law of refraction to Brewster's angle	variable	https://en.wikipedia.org/wiki/Angle	0	0	0	0	0	0
0000003569	\(m_{\rm satellite}\) m_{\rm satellite}	mass of satellite		real	any	5563580265 4627284246 4072200527	radius for satellite in geostationary orbit	variable	https://en.wikipedia.org/wiki/Mass	0	0	1	0	0	0
0000003652	\(x_f\) x_f	final position on x axis		real	any	3485125659 2378095808	angle of maximum distance for projectile motion	variable		0	1	0	0	0	0
0000003852	\(x_1\) x_1	position 1		real	any	9337785146 7734996511 7267155233 4669290568	time invariant force conserves energy	variable		0	1	0	0	0	0
0000003935	\(\rho\) \rho	density		real	any	9999999981 9919999981 8908736791 8688588981 8090924099 6504442697 4560648264	upper limit on velocity in condensed matter Maxwell equations to electric field wave equation	variable	https://en.wikipedia.org/wiki/Density	0	-3	1	0	0	0
0000003978	\(I_1\) I_1	electric current		real	any	6753224061 4128500715 2051901211	total electrical resistance for circuit with two resistors in parallel	variable	https://en.wikipedia.org/wiki/Electric_current	-1	0	0	1	0	0
0000003981	\(h\) h	index		integer	any			variable		0	0	0	0	0	0
0000004037	\(x\) x	position		real	any	2096918413 2334518266 2944838499 2983053062 3253234559 3274926090 3426941928 3512166162 3566149658 4139999399 4287102261 4428528271 4447113478 5438722682 5542528160 5902985919 6131764194 6715248283 6935745841 7354529102 7564894985 7572664728 7575738420 7652131521 7741202861 8405272745 8484544728 8486706976 8582885111 8604483515 8655294002 8849289982 8953094349 8991236357 9805063945 9882526611 0439492440 1202310110 1202312210 1306360899 1586866563 1935543849 1974334644	particle in a 1D box time invariant force conserves energy escape velocity equations of motion in 2D (calculus) angle of maximum distance for projectile motion radius for satellite in geostationary orbit velocity at distance r of object dropped from infinity mass of the Earth Lorentz transformation equation of motion for a spring projectile path in 2D is parabolic work and force and energy Euler equation: trig square root	variable	https://en.wikipedia.org/wiki/Position_(geometry)	0	1	0	0	0	0
0000004065	\(\langle \psi\|\) \langle \psi\|	bra		complex	any	1010393913 9999999975 4948934890 2394935835	quantum basics Hermitian operators have realvalued observables	variable	https://en.wikipedia.org/wiki/Bra%E2%80%93ket_notation	0	0	0	0	0	0
0000004082	\(v_{\rm satellite}\) v_{\rm satellite}	velocity of satellite		real	any	4627284246 4072200527 1994296484	radius for satellite in geostationary orbit	variable	https://en.wikipedia.org/wiki/Velocity	-1	1	0	0	0	0
0000004093	\(PE_1\) PE_1	kinetic energy		real	any	9749777192 8960645192 7734996511 7267155233 5514556106 4872970974 4669290568 4303372136 2770069250	time invariant force conserves energy escape velocity	variable	https://en.wikipedia.org/wiki/Potential_energy	-2	2	1	0	0	0
0000004121	\(KE_{\rm initial}\) KE_{\rm initial}	initial kinetic energy		real	any	9510328252 8049905441 6091977310 5779256336	velocity at distance r of object dropped from infinity	variable	https://en.wikipedia.org/wiki/Kinetic_energy	0	0	0	0	0	0
0000004183	\(F_{\rm spring}\) F_{\rm spring}	force of a spring		real	any	4428528271	equation of motion for a spring	variable	https://en.wikipedia.org/wiki/Hooke%27s_law	-2	1	1	0	0	0
0000004200	\(f\) f			real	any			variable		0	0	0	0	0	0
0000004201	\(f\) f	frequency		real	any	1020394902 0404050504 3147472131 3131211131 3131111133 2131616531 2113211456	derivation of Schrodinger Equation frequency relations frequency and period	variable	https://en.wikipedia.org/wiki/Frequency	-1	0	0	0	0	0
0000004202	\(F\) F	force		real	any	1219718533 7222189955 4664063894 1590774089 9226945488 8661803554 7734996511 7267155233 6935745841 6715248283 5902985919 5542528160 5345738321 4872970974 4800170179 4669290568 3591237106 3512166162 2186083170 2484824786 2431507955 6923310769	Newton's Second Law of Motion: vector to scalar time invariant force conserves energy escape velocity Newton's Law of Gravitation radius for satellite in geostationary orbit velocity at distance r of object dropped from infinity mass of the Earth equation of motion for a spring work and force and energy	variable	https://en.wikipedia.org/wiki/Force	-2	1	1	0	0	0
0000004221	\(u\) u			real	any	8489593964 8489593962 8489593960 8489593958	integration by parts	variable		0	0	0	0	0	0
0000004231	\(c\) c			real	any	9999999969 9999999968 9582958294 9582958293 9385938295 9285928292 5982958249 5982958248 5958392859 5938459282 5928292841	quadratic equation derivation	variable		0	0	0	0	0	0
0000004291	\(g\) g			real	any			variable		0	0	0	0	0	0
0000004306	\(z'\) z'	position in moving reference frame		real	any	1201689765 8515803375	Lorentz transformation	variable	https://en.wikipedia.org/wiki/Frame_of_reference	0	1	0	0	0	0
0000004413	\(h\) h	Planck's constant		real	any	1020394902 1020394900 9999999960 4147472132 3121234212	derivation of Schrodinger Equation	variable	https://en.wikipedia.org/wiki/Planck_constant	-1	2	1	0	0	0
0000004453	\(A\) A	none		complex	any	1525861537 1357848476 1172039918 1020854560 8497631728 8396997949 8283354808 8065128065 8046208134 7621705408 6555185548 6529793063 6306552185 6240206408 5125940051 4075539836 3085575328 3060393541 2236639474 2719691582	double intensity when phase is coherent (optics)	variable	https://farside.ph.utexas.edu/teaching/315/Waveshtml/node88.html	0	0	0	0	0	0
0000004501	\(I\) I	electric current		real	any	7675171493 6061695358 4939880586 4087145886 2715678478	total electrical resistance for circuit with two resistors in parallel total electrical resistance for circuit with two resistors in series	variable	https://en.wikipedia.org/wiki/Electric_current	-1	0	0	1	0	0
0000004518	\(r_{\rm Schwarzschild}\) r_{\rm Schwarzschild}	Schwarzschild radius; event horizon		real	any	6800170830 4275004561 2883079365	Schwarzschild radius for non-rotating black hole	variable	https://en.wikipedia.org/wiki/Schwarzschild_radius	0	1	0	0	0	0
0000004550	\(E_2\) E_2	energy 2		real	any	1809909100 1772416655 8558338742 7875206161 5514556106 3806977900 3591237106 2770069250	time invariant force conserves energy escape velocity	variable		-2	2	1	0	0	0
0000004567	\(c\) c	speed of light in vacuum		real	any	1935543849 1916173354 1639827492 1586866563 1528310784 1201689765 9805063945 9485384858 8360117126 8106885760 7906112355 7701249282 7513513483 6800170830 5838268428 5789289057 5763749235 4585828572 4287102261 4275004561 3485475729 3182633789 2417941373 2999795755 2897612567 2883079365 2542420160	electric field wave equation: from time dependent to time independent Schwarzschild radius for non-rotating black hole Lorentz transformation upper limit on velocity in condensed matter	constant	https://en.wikipedia.org/wiki/Speed_of_light and https://www.wikidata.org/wiki/Q2111 and https://id.loc.gov/authorities/subjects/sh85076878.html	-1	1	0	0	0	0
0000004568	\(t_0\) t_0	time 0		real	any			variable		1	0	0	0	0	0
0000004610	\(\mu_T\) \mu_T	isothermal Joule-Thomson coefficient		real	any			variable	https://en.wikipedia.org/wiki/Joule%E2%80%93Thomson_effect	0	0	0	0	0	0
0000004621	\(i\) i	imaginary unit		imaginary	any	8747785338 1858578388 1648958381 1357848476 9894826550 9848294829 9848292229 9499428242 9492920340 9485384858 9483928192 9482984922 9482943948 9482923849 9482113948 9429829482 9180861128 2501591100 2029293929 2700934933 2103023049 2123139121 2258485859 2394853829 3085575328 3331824625 3470587782 3660957533 3829492824 3942849294 3948571256 3948574224 3948574226 3948574228 3948574230 3948574233 4182362050 4192519596 4341171256 4348571256 4394958389 4504256452 4585932229 4598294821 4638429483 4742644828 4805233006 4838429483 4843995999 4878728014 4923339482 4928239482 4938429482 4938429483 4938429484 4943571230 4985825552 5323719091 5985371230 6555185548 6885625907 7621705408 8332931442 8418527415 8483686863 8651044341 8699789241	derivation of Schrodinger Equation electric field wave equation: from time dependent to time independent identity sin(2 x) = 2 sin(x) cos(x) using Euler's equation Euler equation to exp(i pi) + 1 = 0 double intensity when phase is coherent (optics) hyperbolic trigonometric identities Euler equation proof Euler equation: trig square root Euler equation: trigonometric relations	variable	https://en.wikipedia.org/wiki/Imaginary_unit	0	0	0	0	0	0
0000004635	\(v_u\) v_u	upper limit on velocity in condensed matter		real	any	7701249282	upper limit on velocity in condensed matter	constant	https://arxiv.org/pdf/2004.04818.pdf	-1	1	0	0	0	0
0000004645	\(\kappa_T\) \kappa_T	coefficient of isothermal compressibility		real	any	1190768176 9847143017 9781951738 9718685793 8368984890 3605073197	coefficient of isothermal compressibility using the equation of state for an ideal gas first law of thermodynamics	variable		0	0	0	0	0	0
0000004679	\(\langle \psi_{\alpha} \|\) \langle \psi_{\alpha} \|	bra		complex	any	1395858355 1203938249 1010393944 9596004948 2394935831 2394240499	quantum basics orthogonality	variable	https://en.wikipedia.org/wiki/Bra%E2%80%93ket_notation	0	0	0	0	0	0
0000004686	\(\alpha\) \alpha	expansion coefficient		real	any	1311403394 6925244346 6397683463 5962145508 3464107376 2472653783	coefficient of thermal expansion using the equation of state for an ideal gas first law of thermodynamics	variable	https://en.wikipedia.org/wiki/Thermal_expansion	0	0	0	0	0	-1
0000004691	\(V_{\rm total}\) V_{\rm total}	voltage		real	any	9063568209 4939880586	total electrical resistance for circuit with two resistors in series	variable	https://en.wikipedia.org/wiki/Voltage	-2	2	1	-1	0	0
0000004698	\(B\) B	none		complex	any	1525861537 1020854560 8497631728 8396997949 8283354808 8065128065 7621705408 7107090465 6306552185 6240206408 5125940051 4504256452 4192519596 3085575328 2236639474 2719691582	double intensity when phase is coherent (optics)	variable	https://farside.ph.utexas.edu/teaching/315/Waveshtml/node88.html	0	0	0	0	0	0
0000004711	\(dt\) dt	differential time		real	any	1963253044 8145337879	equations of motion in 2D (calculus)	variable		1	0	0	0	0	0
0000004770	\(v_2\) v_2	velocity 2		real	any	9413699705 9397152918 9356924046 7735737409 7676652285 5733146966 4811121942 4648451961 4270680309 3253234559 2857430695	time invariant force conserves energy work and force and energy	variable	https://en.wikipedia.org/wiki/Velocity	-1	1	0	0	0	0
0000004851	\(m_2\) m_2	mass		real	any	8617866819 7222189955 1292735067 9070394000 8604483515 8405272745 7672365885 7112646057 6935745841 6892595652 6829281943 6268336290 5902985919 5846639423 5693047217 5658865948 5596822289 5128670694 4447113478 4393670960 3896798826 3649797559 3566149658 2217103163 2061086175 2005061870	escape velocity Newton's Law of Gravitation radius for satellite in geostationary orbit velocity at distance r of object dropped from infinity mass of the Earth Kepler's Third Law: period squared propto distance cubed	variable	https://en.wikipedia.org/wiki/Mass	0	0	1	0	0	0
0000004856	\(I_2\) I_2	electric current		real	any	9243879541 7002609475 6753224061	total electrical resistance for circuit with two resistors in parallel	variable	https://en.wikipedia.org/wiki/Electric_current	-1	0	0	1	0	0
0000004928	\(\theta_{\rm Brewster}\) \theta_{\rm Brewster}	Brewster's angle		real	any	1310571337 9756089533 8945218208 8495187962 7696214507 6831637424 4501377629 3417126140 3061811650 2768857871 2575937347	optics: Law of refraction to Brewster's angle	variable	https://en.wikipedia.org/wiki/Brewster%27s_angle	0	0	0	0	0	0
0000004929	\(KE\) KE	kinetic energy		real	any	8357234146 5136652623	time invariant force conserves energy escape velocity velocity at distance r of object dropped from infinity	variable	https://en.wikipedia.org/wiki/Kinetic_energy	-2	2	1	0	0	0
0000004930	\(PE\) PE	potential energy		real	any	6715248283 5136652623	time invariant force conserves energy	variable	https://en.wikipedia.org/wiki/Potential_energy	-2	2	1	0	0	0
0000004931	\(E\) E	energy		real	any	1020394902 9999999965 9999999961 5136652623 4298359851 4298359845 4298359835 4147472132	derivation of Schrodinger Equation time invariant force conserves energy	variable	https://en.wikipedia.org/wiki/Energy and https://www.wikidata.org/wiki/Q11379 and https://schema.org/Energy	-2	2	1	0	0	0
0000004933	\(K_{\rm equilibrium}\) K_{\rm equilibrium}	constant for equilibrium when rate of adsorption equals the rate of desorption		real	any	7928111771 7924063906 7517073655 7267424860 6457999644 6240546932 4689334676	Langmuir Adsorption	variable	https://en.wikipedia.org/wiki/Langmuir_adsorption_model	0	0	0	0	0	0
0000004940	\([A_{\rm adsorption}]\) [A_{\rm adsorption}]	surface concentration of A in molecules per square meter		real	any	9562264720 8131665171 7517073655 6955192897 6457999644 5085809757 4301729661 3599953931 3488423948 2168306601 2114909846	Langmuir Adsorption	variable	https://en.wikipedia.org/wiki/Langmuir_adsorption_model	0	2	0	0	1	0
0000004989	\(t'\) t'	time in moving reference frame		real	any	1201689765 7741202861 4139999399 3426941928 2983053062 2096918413 1974334644	Lorentz transformation	variable		1	0	0	0	0	0
0000005005	\(d v_x\) d v_x	differential velocity along x axis		real	any	1166310428 2366691988	equations of motion in 2D (calculus)	variable		-1	1	0	0	0	0
0000005022	\(m_1\) m_1	mass		real	any	8617866819 4664063894 1811867899 1292735067 9838128064 9170048197 9152823411 9081138616 9070394000 8604483515 8552710882 8405272745 6935745841 6892595652 6829281943 6091977310 5902985919 5658865948 5596822289 5128670694 4947831649 4447113478 4393670960 4188580242 3896798826 3781109867 3566149658 2906548078 2217103163 2061086175	escape velocity Newton's Law of Gravitation radius for satellite in geostationary orbit velocity at distance r of object dropped from infinity mass of the Earth Kepler's Third Law: period squared propto distance cubed	variable	https://en.wikipedia.org/wiki/Mass	0	0	1	0	0	0
0000005153	\(v_0\) v_0	initial velocity		real	any	1967582749 1265150401 1191796961 1087417579 9973952056 9897284307 9862900242 9759901995 9658195023 8949329361 8922441655 8706092970 8269198922 8198310977 7939765107 7391837535 7376526845 7233558441 7215099603 7011114072 6457044853 6175547907 6083821265 5733721198 5611024898 5438722682 5379546684 5353282496 4948763856 4798787814 4778077984 4748157455 4268085801 3607070319 3485125659 3462972452 3366703541 2297105551 2086924031	equations of motion in 2D (calculus) angle of maximum distance for projectile motion equations of motion in 1D with constant acceleration - SUVAT (algebra) work and force and energy	variable		-1	1	0	0	0	0
0000005156	\(m\) m	mass		real	any	1772973171 0007455074 1931103031 1888494137 1784114349 6923310769 2484824786 2042298788 2148049269 2883079365 2334518266 3004158505 3650370389 3846041519 4267808354 4270680309 4275004561 4298359835 4298359845 4298359851 4341171256 4348571256 4393258808 4784793837 4800170179 4811121942 4928007622 5345738321 5404822208 5733146966 5868688585 5978756813 6026694087 6131764194 6800170830 6870322215 6908055431 7676652285 7735737409 7749253510 8357234146 8655294002 8661803554 8946383937 8953094349 8991236357 9226945488 9356924046 9407192813 9413699705 9703482302 9958485859 1029039903 1029039904 1158485859	Newton's Second Law of Motion: vector to scalar derivation of Schrodinger Equation time invariant force conserves energy escape velocity Schwarzschild radius for non-rotating black hole Newton's Law of Gravitation radius for satellite in geostationary orbit velocity at distance r of object dropped from infinity mass of the Earth equation of motion for a spring Kepler's Third Law: period squared propto distance cubed work and force and energy	variable	https://en.wikipedia.org/wiki/Mass and https://www.wikidata.org/wiki/Q11423 and https://schema.org/Mass	0	0	1	0	0	0
0000005177	\(v\) v	none		real	any	8489593964	integration by parts	variable		0	0	0	0	0	0
0000005321	\(k\) k	angular wavenumber		real	any	1858772113 1020010291 1010923823 0934990943 9999999962 9999999870 8582885111 8575748999 5900595848 3948574224 3121513111 3121234212 3121234211	derivation of Schrodinger Equation frequency relations particle in a 1D box	variable	https://en.wikipedia.org/wiki/Wavenumber	0	-1	0	0	0	0
0000005332	\(KE_{\rm escape}\) KE_{\rm escape}	kinetic energy of escape velocity		real	any	6870322215 2503972039	escape velocity	variable		-2	2	1	0	0	0
0000005340	\(KE_{\rm final}\) KE_{\rm final}	final kinetic energy		real	any	8552710882 8049905441 5850144586 5779256336	velocity at distance r of object dropped from infinity	variable	https://en.wikipedia.org/wiki/Kinetic_energy	0	0	0	0	0	0
0000005344	\(t_{\rm Earth\ orbit}\) t_{\rm Earth\ orbit}	time of Earth's orbit around sun		real	any	8721295221 7175416299 3080027960 3046191961	speed of Earth around Sun	variable		1	0	0	0	0	0
0000005456	\(x'\) x'	position in moving reference frame		real	any	1201689765 4662369843 2983053062	Lorentz transformation	variable	https://en.wikipedia.org/wiki/Frame_of_reference	0	1	0	0	0	0
0000005458	\(m_{\rm Earth}\) m_{\rm Earth}	mass of Earth		real	any	1559688463 1330874553 1143343287 1132941271 9703482302 9440616166 9412953728 9407192813 8661803554 7846240076 7749253510 7112613117 7010294143 6131764194 5978756813 5563580265 4858693811 4072200527 3906710072 3846041519 3364286646 2977457786 2308660627 2750380042 2617541067 2042298788 1994296484	escape velocity radius for satellite in geostationary orbit mass of the Earth	constant	https://en.wikipedia.org/wiki/Earth	0	0	2	0	0	0
0000005467	\(x_2\) x_2	position 2		real	any	9337785146 7734996511 7267155233 2431507955	time invariant force conserves energy	variable		0	1	0	0	0	0
0000005480	\(\pi_T\) \pi_T	internal pressure at constant temperature		real	any	5634116660 5002539602	first law of thermodynamics	variable	https://en.wikipedia.org/wiki/Internal_pressure	-2	1	1	0	0	0
0000005505	\(v_x\) v_x	velocity along x axis		real	any	1819663717 1676472948 8750379055 8460820419 7729413831 6134836751 5349866551	equations of motion in 2D (calculus)	variable		-1	1	0	0	0	0
0000005563	\(t_i\) t_i	initial time		real	any			variable		1	0	0	0	0	0
0000005579	\(E_1\) E_1	energy 1		real	any	1809909100 1772416655 8558338742 5514556106 4303372136 3806977900 2770069250	time invariant force conserves energy escape velocity	variable		-2	2	1	0	0	0
0000005595	\(T_{\rm geostationary\ orbit}\) T_{\rm geostationary\ orbit}	geostationary orbital period		real	any	1559688463 3920616792	radius for satellite in geostationary orbit	variable	https://en.wikipedia.org/wiki/Orbital_period	1	0	0	0	0	0
0000005598	\(\hat{A}\) \hat{A}	observerable operator		real	any	1010393913 9596004948 9294858532	quantum basics Hermitian operators have realvalued observables quantum basics orthogonality	variable	https://en.wikipedia.org/wiki/Operator_(physics)	0	0	0	0	0	0
0000005647	\(y\) y	position		real	any	1935543849 1586866563 1405465835 9862900242 9805063945 8808860551 7354529102 7252338326 7057864873 6204539227 4287102261 2858549874 2461349007	equations of motion in 2D (calculus) angle of maximum distance for projectile motion Lorentz transformation projectile path in 2D is parabolic	variable	https://en.wikipedia.org/wiki/Position_(geometry)	0	1	0	0	0	0
0000005674	\(d v_y\) d v_y	differential velocity along y axis		real	any	1702349646 8584698994	equations of motion in 2D (calculus)	variable		-1	1	0	0	0	0
0000005734	\(\Delta KE\) \Delta KE	change in kinetic energy		real	any	1114820451 8049905441	velocity at distance r of object dropped from infinity	variable	https://en.wikipedia.org/wiki/Kinetic_energy	0	0	0	0	0	0
0000005786	\(U\) U	internal energy		real	any	1815398659 1085150613 9941599459 7826132469 6055078815 5634116660 2257410739	first law of thermodynamics	variable	https://en.wikipedia.org/wiki/Internal_energy	-2	2	1	0	0	0
0000005842	\(dy\) dy	differential displacement along y axis		real	any	9848292229 8145337879	equations of motion in 2D (calculus) Euler equation proof	variable		0	1	0	0	0	0
0000005854	\(a\) a	atomic separation		real	any	9376481176 8908736791 8688588981 8090924099	upper limit on velocity in condensed matter	variable		0	1	0	0	0	0
0000005916	\(m_p\) m_p	mass of proton		real	any	7701249282 5646314683 2897612567	upper limit on velocity in condensed matter	constant	https://en.wikipedia.org/wiki/Proton	0	0	1	0	0	0
0000006022	\(N_A\) N_A	Avagadro's constant		real	any			constant	https://en.wikipedia.org/wiki/Avogadro_constant	0	0	0	0	-1	0
0000006081	\(r_{\rm Earth\ orbit}\) r_{\rm Earth\ orbit}	radius of Earth's orbit		real	any	6348260313 4593428198 3472836147 3080027960	speed of Earth around Sun	constant	https://en.wikipedia.org/wiki/Earth%27s_orbit	0	1	0	0	0	0
0000006191	\(W_{\rm by\ system}\) W_{\rm by\ system}	work done by system		real	any	1114820451 9081138616 5850144586 5779256336 2907404069	velocity at distance r of object dropped from infinity	variable	https://en.wikipedia.org/wiki/Work_(physics)	-2	2	1	0	0	0
0000006197	\(\mu_0\) \mu_0	vacuum permeability, permeability of free space, permeability of vacuum, or magnetic constant		real	any	1858578388 9991999979 9394939493 9291999979 8494839423 4985825552 4585828572 2029293929	electric field wave equation: from time dependent to time independent Maxwell equations to electric field wave equation	constant	https://en.wikipedia.org/wiki/Vacuum_permeability	0	1	1	-2	0	0
0000006235	\(f\) f	proportionality constant		real	any	9376481176 8090924099 7837519722	upper limit on velocity in condensed matter	variable		0	0	0	0	0	0
0000006238	\(E\) E	electric field		real	any	1858578388 9991999979 9499428242 9485384858 9394939493 8572852424 7575859310 7575859308 7575859306 7575859302 7575859295 7466829492 4985825552 4943571230 3948574233 3948574230 3948574228 3948571256 3485475729 2029293929	curl curl identity derivation of Schrodinger Equation electric field wave equation: from time dependent to time independent Maxwell equations to electric field wave equation	variable	https://en.wikipedia.org/wiki/Electric_field	0	0	0	0	0	0
0000006277	\(G\) G	gravitational constant		real	any	9703482302 1811867899 1559688463 1330874553 1292735067 1143343287 9838128064 1994296484 2005061870 2042298788 2617541067 2061086175 2750380042 2883079365 2308660627 2906548078 2977457786 3566149658 3781109867 3846041519 3896798826 3906710072 4072200527 4188580242 4275004561 4393670960 4447113478 4858693811 5404822208 5563580265 5596822289 5658865948 5693047217 5732331610 5846639423 5902985919 5978756813 6131764194 6204539227 6800170830 6829281943 6892595652 6935745841 7010294143 7112646057 7749253510 7846240076 8405272745 8604483515 8661803554 8946383937 9070394000 9152823411 9170048197 9407192813 9412953728 9440616166	escape velocity Schwarzschild radius for non-rotating black hole equations of motion in 2D (calculus) Newton's Law of Gravitation radius for satellite in geostationary orbit velocity at distance r of object dropped from infinity mass of the Earth Kepler's Third Law: period squared propto distance cubed	constant	https://en.wikipedia.org/wiki/Gravitational_constant	-2	3	-1	0	0	0
0000006431	\(PE_{\rm Earth\ surface}\) PE_{\rm Earth\ surface}	potential energy at the Earth's surface		real	any	7573835180 3846041519 2503972039	escape velocity	variable		-2	2	1	0	0	0
0000006458	\(R\) R	electrical resistance		real	any	4087145886	total electrical resistance for circuit with two resistors in parallel total electrical resistance for circuit with two resistors in series	variable	https://en.wikipedia.org/wiki/Electrical_resistance_and_conductance	-1	2	1	-2	0	0
0000006599	\(V\) V	voltage		real	any	9243879541 7002609475 4866160902 4128500715 4087145886 2271186630 2809345867 2051901211	total electrical resistance for circuit with two resistors in parallel total electrical resistance for circuit with two resistors in series	variable	https://en.wikipedia.org/wiki/Voltage	-2	2	1	-1	0	0
0000006682	\(C_V\) C_V	heat capacity at constant volume		real	any	1085150613 5002539602	first law of thermodynamics	variable	https://en.wikipedia.org/wiki/Heat_capacity	-2	2	1	0	0	-1
0000006687	\(r_{\rm adsorption}\) r_{\rm adsorption}	rate of adsorption		real	any	6783009163 3736177473	Langmuir Adsorption	variable	https://en.wikipedia.org/wiki/Langmuir_adsorption_model	-1	0	0	0	0	0
0000006694	\(dv\) dv	differential of v		real	any			variable		0	0	0	0	0	0
0000006709	\(v_{\rm average}\) v_{\rm average}	velocity average		real	any	6175547907 3411994811	Newton's Law of Gravitation equations of motion in 1D with constant acceleration - SUVAT (algebra)	variable	https://en.wikipedia.org/wiki/Velocity	-1	1	0	0	0	0
0000006722	\(du\) du	differential of u		real	any			variable		0	0	0	0	0	0
0000006728	\(z\) z	position		real	any	1935543849 1586866563 9805063945 8515803375 4287102261	Lorentz transformation	variable	https://en.wikipedia.org/wiki/Position_(geometry)	0	1	0	0	0	0
0000006789	\(W\) W	work		real	any	9413699705 8953094349 7749253510 7573835180 5978756813 5542528160 4811121942 4447113478 3512166162 3360172339	escape velocity work and force and energy	variable	https://en.wikipedia.org/wiki/Work_(physics)	-2	2	1	0	0	0
0000006799	\({\cal H}\) {\cal H}	operator		complex	any	2258485859	derivation of Schrodinger Equation	variable	https://en.wikipedia.org/wiki/Hamiltonian_(quantum_mechanics)	0	0	0	0	0	0
0000006850	\(k_{\rm adsorption}\) k_{\rm adsorption}	constant of forward adsorption reaction		real	any	9562264720 7924063906 6240546932 5085809757 4301729661 3736177473 3507029294 3488423948 2168306601	Langmuir Adsorption	variable	https://en.wikipedia.org/wiki/Langmuir_adsorption_model	0	0	0	0	0	0
0000007055	\(a_y\) a_y	acceleration along y axis		real	any	8602512487 8228733125 7729413831 2741489181	equations of motion in 2D (calculus)	variable	https://en.wikipedia.org/wiki/Acceleration	-2	1	0	0	0	0
0000007092	\(y_f\) y_f	final position on y axis		real	any	9112191201 5379546684	angle of maximum distance for projectile motion	variable		0	1	0	0	0	0
0000007110	\(r_{\rm geostationary\ orbit}\) r_{\rm geostationary\ orbit}	geostationary orbital radius		real	any	1559688463	radius for satellite in geostationary orbit	variable	https://en.wikipedia.org/wiki/Geostationary_orbit	0	1	0	0	0	0
0000007159	\(a_x\) a_x	acceleration along x axis		real	any	1819663717 9707028061 8602512487 7729413831	equations of motion in 2D (calculus)	variable	https://en.wikipedia.org/wiki/Acceleration	-2	1	0	0	0	0
0000007343	\(T\) T	temperature		real	any	1311403394 1190768176 1085150613 9941599459 8435841627 8368984890 7826132469 6925244346 6397683463 6055078815 3605073197 3497828859 3464107376 2257410739 2613006036 2472653783	coefficient of thermal expansion using the equation of state for an ideal gas coefficient of isothermal compressibility using the equation of state for an ideal gas first law of thermodynamics	variable	https://en.wikipedia.org/wiki/Temperature	0	0	0	0	0	1
0000007427	\(v_{\rm Earth\ orbit}\) v_{\rm Earth\ orbit}	velocity of Earth's orbit around sun		real	any	6998364753 4593428198 4180845508 3080027960 3046191961	speed of Earth around Sun	variable		-1	1	0	0	0	0
0000007545	\(\theta_2\) \theta_2	angle		real	any	6450985774	optics: Law of refraction to Brewster's angle	variable	https://en.wikipedia.org/wiki/Angle	0	0	0	0	0	0
0000007557	\(g_{\rm Earth}\) g_{\rm Earth}	average acceleration due to gravity on Earth		real	any	9440616166 9407192813 4800170179 2308660627	mass of the Earth	constant	https://en.wikipedia.org/wiki/Gravity_of_Earth	-2	1	0	0	0	0
0000007586	\(V\) V	volume		real	any	1311403394 1190768176 9781951738 8435841627 8368984890 6925244346 6397683463 5962145508 5634116660 3605073197 3497828859 3464107376 2613006036	coefficient of thermal expansion using the equation of state for an ideal gas coefficient of isothermal compressibility using the equation of state for an ideal gas first law of thermodynamics	variable	https://en.wikipedia.org/wiki/Volume_(thermodynamics)	0	3	0	0	0	0
0000007652	\(d_1\) d_1	distance		real	any	5586102077 5128670694 4188580242 3781109867 2906548078 2217103163	Kepler's Third Law: period squared propto distance cubed	variable	https://en.wikipedia.org/wiki/Distance	0	1	0	0	0	0
0000007752	\(a_{\beta}\) a_{\beta}	none		complex	any	1203938249 1010393944 3924948349 2394935831 2394240499	quantum basics orthogonality	variable	https://en.wikipedia.org/wiki/Quantum_mechanics	0	0	0	0	0	0
0000007882	\(I\) I	intensity		real	any	1525861537 1020854560 8497631728 8396997949 8065128065 7621705408 6306552185 5125940051 3085575328	double intensity when phase is coherent (optics)	variable	https://en.wikipedia.org/wiki/Intensity_(physics)	-3	0	1	0	0	0
0000007930	\(m\) m	index		integer	any	7575859310 7575859308 7575859306 7575859304 7575859302	curl curl identity	variable		0	0	0	0	0	0
0000007940	\(\epsilon_0\) \epsilon_0	vacuum permittivity, permittivity of free space or electric constant or the distributed capacitance of the vacuum		real	any	1858578388 1556389363 1314864131 9999999981 9640720571 9394939493 8494839423 8106885760 5838268428 4985825552 4585828572 3935058307 3291685884 2029293929	electric field wave equation: from time dependent to time independent upper limit on velocity in condensed matter Maxwell equations to electric field wave equation	constant	https://en.wikipedia.org/wiki/Vacuum_permittivity	2	-3	-1	2	0	0
0000007984	\(i\) i	index		integer	any	7575859304	curl curl identity	variable		0	0	0	0	0	0
0000008039	\(H\) H	enthalpy		real	any			variable	https://en.wikipedia.org/wiki/Enthalpy	-2	2	1	0	0	0
0000008134	\(P\) P	pressure		real	any	1311403394 1190768176 9847143017 9781951738 9718685793 8435841627 8368984890 6925244346 5962145508 3605073197 3497828859 2613006036	coefficient of thermal expansion using the equation of state for an ideal gas coefficient of isothermal compressibility using the equation of state for an ideal gas first law of thermodynamics	variable	https://en.wikipedia.org/wiki/Pressure	-2	-1	1	0	0	0
0000008179	\(R\) R	ideal gas constant		real	any	1311403394 1190768176 8435841627 8368984890 5962145508 3605073197 3497828859 2613006036	coefficient of thermal expansion using the equation of state for an ideal gas coefficient of isothermal compressibility using the equation of state for an ideal gas	constant	https://en.wikipedia.org/wiki/Gas_constant	-2	2	1	0	-1	-1
0000008251	\(I_{\rm coherent}\) I_{\rm coherent}	intensity of coherent waves		real	any	1172039918 8283354808 8046208134 6556875579	double intensity when phase is coherent (optics)	variable	https://en.wikipedia.org/wiki/Intensity_(physics)	-3	0	1	0	0	0
0000008257	\(V_1\) V_1	voltage		real	any	9063568209 7675171493	total electrical resistance for circuit with two resistors in series	variable	https://en.wikipedia.org/wiki/Voltage	-2	2	1	-1	0	0
0000008304	\(l\) l	index		integer	any	7575859308 7575859306 7575859304	curl curl identity	variable		0	0	0	0	0	0
0000008330	\(\psi_0\) \psi_0	amplitude of wavefunction		complex	any	4943571230 3948574233 3948574230 3948574228 3948574226 3948574224	derivation of Schrodinger Equation	variable		0	0	0	0	0	0
0000008339	\(\hat{x}\) \hat{x}	unit vector		real	any	9341391925 8602512487 7729413831 5349866551	equations of motion in 2D (calculus)	variable	https://en.wikipedia.org/wiki/Unit_vector	0	0	0	0	0	0
0000008349	\(\hat{x}_i\) \hat{x}_i	ith unit vector		real	any	7575859308 7575859306 7575859302	curl curl identity	variable		0	0	0	0	0	0
0000008379	\(k_{\rm desorption}\) k_{\rm desorption}	constant of backward desorption reaction		real	any	9562264720 7924063906 6955192897 6240546932 5085809757 4301729661 3488423948 2168306601	Langmuir Adsorption	variable	https://en.wikipedia.org/wiki/Langmuir_adsorption_model	0	0	0	0	0	0
0000008586	\(\phi\) \phi	angle		real	any	8602221482 8497631728 7621705408 6774684564 4504256452 4192519596 3660957533 3085575328 2700934933	double intensity when phase is coherent (optics)	variable	https://en.wikipedia.org/wiki/Angle	0	0	0	0	0	0
0000008656	\(v_{\rm escape}\) v_{\rm escape}	escape velocity		real	any	1330874553 1143343287 9703482302 9412953728 8946383937 6870322215 5404822208 2977457786 2750380042 2042298788	escape velocity Schwarzschild radius for non-rotating black hole	variable	https://en.wikipedia.org/wiki/Escape_velocity	-1	1	0	0	0	0
0000008697	\(R_1\) R_1	electrical resistance		real	any	1457415749 7675171493 7217021879 4866160902 4128500715 2715678478 2051901211	total electrical resistance for circuit with two resistors in parallel total electrical resistance for circuit with two resistors in series	variable	https://en.wikipedia.org/wiki/Electrical_resistance_and_conductance	-1	2	1	-2	0	0
0000008721	\(V_2\) V_2	voltage		real	any	9063568209 6061695358	total electrical resistance for circuit with two resistors in series	variable	https://en.wikipedia.org/wiki/Voltage	-2	2	1	-1	0	0
0000008762	\(T_{\rm orbit}\) T_{\rm orbit}	orbital period		real	any	8059639673 7672365885 7010294143 6268336290 5177311762 4858693811 3906710072 3650370389 3614055652 3004158505 2617541067	Newton's Law of Gravitation radius for satellite in geostationary orbit	variable	https://en.wikipedia.org/wiki/Orbital_period	1	0	0	0	0	0
0000008849	\(PE_2\) PE_2	potential energy		real	any	8960645192 7875206161 7734996511 7267155233 5514556106 4872970974 2267521164 2770069250 2431507955	time invariant force conserves energy escape velocity	variable	https://en.wikipedia.org/wiki/Potential_energy	-2	2	1	0	0	0
0000008909	\(v_{\rm final}\) v_{\rm final}	final velocity		real	any	9081138616 8552710882 7112646057 6892595652 5846639423 5693047217 4947831649	velocity at distance r of object dropped from infinity	variable	https://en.wikipedia.org/wiki/Velocity	-1	1	0	0	0	0
0000009046	\(p_A\) p_A	partial pressure of A over the surface		real	any	9562264720 7928111771 7517073655 7267424860 6457999644 5085809757 4689334676 4301729661 3736177473 3507029294 3488423948 2168306601	Langmuir Adsorption	variable	https://en.wikipedia.org/wiki/Langmuir_adsorption_model	0	0	0	0	0	0
0000009067	\([S]\) [S]	concentration of free sites in number per square meter		real	any	9562264720 5085809757 3736177473 3599953931 3507029294 3488423948	Langmuir Adsorption	variable	https://en.wikipedia.org/wiki/Langmuir_adsorption_model	0	-2	0	0	1	0
0000009107	\(v_y\) v_y	velocity along y axis		real	any	1405465835 8228733125 7729413831 7252338326 6572039835 5349866551 1977955751	equations of motion in 2D (calculus) projectile path in 2D is parabolic	variable		-1	1	0	0	0	0
0000009139	\(a\) a			real	any	7764834870 1857710291 1202312210 1202310110 1020010291 1010393913 0948572140 0439492440 0203024440 9999999969 9999999968 9858028950 9582958294 9582958293 9485747246 9485747245 9385938295 9285928292 8889444440 8849289982 8582885111 8577275751 8576785890 8575748999 8485867742 5982958249 5982958248 5959282914 5958392859 5938459282 5928292841 5928285821 5857434758 4857475848 2944838499 2848934890	Euler's equation from MacLaurin series particle in a 1D box quadratic equation derivation quantum basics Hermitian operators have realvalued observables	variable		0	0	0	0	0	0
0000009140	\(a\) a	acceleration		real	any	6831694380 1075552184 1967582749 1265150401 1259826355 9759901995 9658195023 8953094349 8655294002 8269198922 7939765107 7215099603 7011114072 6457044853 6421241247 5733721198 5611024898 5345738321 4948763856 4798787814 4784793837 4748157455 4580545876 3462972452 3366703541 3253234559 2334518266 2857430695	Newton's Second Law of Motion: vector to scalar time invariant force conserves energy Newton's Law of Gravitation equations of motion in 1D with constant acceleration - SUVAT (algebra) mass of the Earth equation of motion for a spring work and force and energy	variable		-2	1	0	0	0	0
0000009189	\(\omega_{\rm Debye}\) \omega_{\rm Debye}	Debye frequency		real	any			variable	https://en.wikipedia.org/wiki/Debye_model#Debye_frequency	0	0	0	0	0	0
0000009199	\(dx\) dx			real	any	1963253044 1934748140 1590774089 1202310110 0948572140 9848292229 9482943948 8604483515 8575748999 8485757728 8460820419 7455581657 5727578862 4857472413	particle in a 1D box escape velocity equations of motion in 2D (calculus) work and force and energy Euler equation proof	variable		0	1	0	0	0	0
0000009329	\(\|\psi \rangle\) \|\psi \rangle	ket		complex	any	1010393913	quantum basics Hermitian operators have realvalued observables	variable	https://en.wikipedia.org/wiki/Bra%E2%80%93ket_notation	0	0	0	0	0	0
0000009372	\(W_{\rm to\ system}\) W_{\rm to\ system}	work done to system		real	any	8405272745 7882872592 5596822289 4947831649 4393670960 3566149658 2907404069 2061086175	velocity at distance r of object dropped from infinity	variable	https://en.wikipedia.org/wiki/Work_(physics)	-2	2	1	0	0	0
0000009398	\(dW\) dW	differential work		real	any	1590774089 8604483515	escape velocity work and force and energy	variable		-2	2	1	0	0	0
0000009431	\(v_{0, y}\) v_{0, y}	initial velocity along y axis		real	any	9973952056 9341391925 8949329361 8808860551 8145337879 7376526845 7354529102 6572039835 6204539227 2858549874 2461349007	equations of motion in 2D (calculus) projectile path in 2D is parabolic	variable	https://en.wikipedia.org/wiki/Velocity	-1	1	0	0	0	0
0000009432	\(Q\) Q	heat flow		real	any	1815398659	first law of thermodynamics	variable	https://en.wikipedia.org/wiki/Heat	-2	2	1	0	0	0
0000009489	\(\psi\) \psi	none		complex	any	1934748140 1648958381 0203024440 9958485859 9585727710 9393939992 9393939991 8849289982 8582885111 8572657110 5985371230 5868688585 4943571230 4394958389 4348571256 4341171256 3948574233 3948574230 3948574228 3948574226 3948574224 3948571256 2395958385 2944838499 2258485859	derivation of Schrodinger Equation particle in a 1D box	variable		0	0	0	0	0	0
0000009491	\(T\) T	period		real	any	1811867899 1772973171 1293923844 0934990943 9838128064 9170048197 9152823411 9070394000 5658865948 4188580242 3781109867 3132131132 3131111133 2906548078 2148049269 2131616531 2113211456	frequency relations equation of motion for a spring Kepler's Third Law: period squared propto distance cubed frequency and period	variable		1	0	0	0	0	0
0000009647	\(I_{\rm total}\) I_{\rm total}	electric current		real	any	6753224061 2271186630 2809345867	total electrical resistance for circuit with two resistors in parallel	variable	https://en.wikipedia.org/wiki/Electric_current	-1	0	0	1	0	0
0000009669	\(\delta\) \delta	Kronecker delta		real	any			variable	https://en.wikipedia.org/wiki/Kronecker_delta	0	0	0	0	0	0
0000009690	\(k\) k	index		integer	any	7575859308 7575859306 7575859304 7575859302	curl curl identity	variable		0	0	0	0	0	0
0000009838	\(E_{\rm Rydberg}\) E_{\rm Rydberg}	Rydberg energy		real	any	1556389363 4107032818	upper limit on velocity in condensed matter	variable	https://en.wikipedia.org/wiki/Rydberg_constant	0	0	0	0	0	0
0000009843	\(\mu_{JT}\) \mu_{JT}	Joule-Thomson coefficient		real	any			variable	https://en.wikipedia.org/wiki/Joule%E2%80%93Thomson_effect#The_Joule%E2%80%93Thomson_(Kelvin)_coefficient	2	1	-1	0	0	1
0000009863	\(m\) m	mass of atom or molecule		real	any	5272284986 9854442418 9640720571 8908736791 8688588981 7837519722 5789289057 5646314683 3935058307	Newton's Second Law of Motion: vector to scalar upper limit on velocity in condensed matter	variable	https://en.wikipedia.org/wiki/Mass	0	0	1	0	0	0
0000009885	\(A\) A	amplitude		real	any	7652131521 6908055431 5945893986 5415824175	equation of motion for a spring	variable	https://en.wikipedia.org/wiki/Amplitude	0	0	0	0	0	0
1777778008	\(c_2\) c_2	constant	constant of solution to differential equation	real	any			variable		0	1	0	0	0	0
2357809348	\(\alpha\) \alpha	angle		real	any			variable		0	0	0	0	0	0
2507344057	\(v_{\rm max}\) v_{\rm max}	maximum velocity		real	any			variable		-1	1	0	0	0	0
3923126873	\(\beta\) \beta	angle		real	any			variable		0	0	0	0	0	0
4133185897	\(c_1\) c_1	constant	constant of solution to differential equation	real	any			variable		0	1	0	0	0	0
4482727458	\(F_{\rm gravity}\) F_{\rm gravity}	force due to gravity		real	any	8617866819	Newton's Law of Gravitation	variable		-2	1	1	0	0	0
6047582651	\(a_{\rm max}\) a_{\rm max}	maximum acceleration		real	any			variable		-2	1	0	0	0	0
8937294510	\(\infty\) \infty	infinity		arbitrary	any	7764834870 8637447837	Euler's equation from MacLaurin series	variable	https://en.wikipedia.org/wiki/Infinity	0	0	0	0	0	0

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