Physics Derivation Graph navigation Sign in

review derivation: Euler equation to e^(i pi) + 1 = 0

This page contains three views of the steps in the derivation: d3js, graphviz PNG, and a table.


Hold the mouse over a node to highlight that node and its neighbors. You can zoom in/out. You can pan the image. You can move nodes by clicking and dragging.

Notes for this derivation:

Options
Alternate views of this derivation:
Edit this content:    

To edit a step, click on the number in the "Index" column in the table below

Clicking on the step index will take you to the page where you can edit that step.

Index Inference Rule Input latex Feeds latex Output latex step validity dimension check unit check notes
3 simplify
  1. 8332931442; locally 1148677:
    \(\exp(i \pi) = \cos(\pi)+i \sin(\pi)\)
    \(e^{pdg_{3141} pdg_{4621}} = pdg_{4621} \sin{\left(pdg_{3141} \right)} + \cos{\left(pdg_{3141} \right)}\)
  1. 6885625907; locally 8524301:
    \(\exp(i \pi) = -1 + i 0\)
    \(e^{pdg_{3141} pdg_{4621}} = -1\)
LHS diff is 0 RHS diff is pdg4621*sin(pdg3141) + cos(pdg3141) + 1 8332931442:
6885625907:
8332931442:
6885625907:
2 change variable X to Y
  1. 4938429483; locally 1580045:
    \(\exp(i x) = \cos(x)+i \sin(x)\)
    \(e^{pdg_{1464} pdg_{4621}} = pdg_{4621} \sin{\left(pdg_{1464} \right)} + \cos{\left(pdg_{1464} \right)}\)
  1. 3268645065:
    \(x\)
    \(pdg_{1464}\)
  2. 9350663581:
    \(\pi\)
    \(pdg_{3141}\)
  1. 8332931442; locally 1148677:
    \(\exp(i \pi) = \cos(\pi)+i \sin(\pi)\)
    \(e^{pdg_{3141} pdg_{4621}} = pdg_{4621} \sin{\left(pdg_{3141} \right)} + \cos{\left(pdg_{3141} \right)}\)
valid 4938429483:
8332931442:
4938429483:
8332931442:
1 declare initial expr
  1. 4938429483; locally 1580045:
    \(\exp(i x) = \cos(x)+i \sin(x)\)
    \(e^{pdg_{1464} pdg_{4621}} = pdg_{4621} \sin{\left(pdg_{1464} \right)} + \cos{\left(pdg_{1464} \right)}\)
no validation is available for declarations 4938429483:
4938429483:
5 add X to both sides
  1. 3331824625; locally 9610540:
    \(\exp(i \pi) = -1\)
    \(e^{pdg_{3141} pdg_{4621}} = -1\)
  1. 4901237716:
    \(1\)
    \(1\)
  1. 2501591100; locally 9472905:
    \(\exp(i \pi) + 1 = 0\)
    \(e^{pdg_{3141} pdg_{4621}} + 1 = 0\)
valid 3331824625:
2501591100: error for dim with 2501591100
3331824625:
2501591100: N/A
4 simplify
  1. 6885625907; locally 8524301:
    \(\exp(i \pi) = -1 + i 0\)
    \(e^{pdg_{3141} pdg_{4621}} = -1\)
  1. 3331824625; locally 9610540:
    \(\exp(i \pi) = -1\)
    \(e^{pdg_{3141} pdg_{4621}} = -1\)
valid 6885625907:
3331824625:
6885625907:
3331824625:
6 declare final expr
  1. 2501591100; locally 9472905:
    \(\exp(i \pi) + 1 = 0\)
    \(e^{pdg_{3141} pdg_{4621}} + 1 = 0\)
no validation is available for declarations 2501591100: error for dim with 2501591100
2501591100: N/A
Physics Derivation Graph: Steps for Euler equation to e^(i pi) + 1 = 0

Symbols for this derivation

See also all 227 symbols
symbol ID category latex scope dimension name value Used in derivations references
1464 variable x
\(x\)
['real'] dimensionless 140
3141 constant \pi
\(\pi\)
['real'] dimensionless pi 3.1415   dimensionless
72
4621 variable i
\(i\)
['imaginary'] dimensionless imaginary unit 74
MESSAGE: