Euler’s Identity
Euler’s Identity is widely considered to be the most beautiful formula in all of mathematics. It connects the numbers e,π, i, 0 and 1 in one compact formula.
At first sight, the identity below might not look particularly stunning. However, its beauty lies in the many ideas that it brings together. One simple formula contains five of the most important numbers in all of mathematics.
In seven symbols, we can see over two thousand years of mathematical thought and development.
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The identity is derived from the formula:
This is a relationship that intimately links trigonometrical and exponential functions in a most unexpected way.
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The imaginary number called ‘i’ is the square root of -1.
‘i’ is the square root of –1
‘e’ is the base of natural logarithms
2.71828182…...
‘π’ is the ratio of the circumference of a circle to its diameter
The term imaginary is unfortunate as we can see that ‘i’ certainly exists as it is linked so closely to the ‘real’ numbers ‘e’ and ‘π’.