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Eulers Identity

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Something to add to your knowledge bank.
The Most Beautiful equation in Maths.

Fascinating..
 
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Yeah well, so what is it used for ?
Essentially the equation pulls together 5 critical mathematical constants :
  • The number 0.
  • The number 1.
  • The number π, an irrational number (with unending digits) that is the ratio of the circumference of a circle to its diameter. It is approximately 3.14159…
  • The number e, also an irrational number. It is the base of natural logarithms that arises naturally through study of compound interest and calculus. The number e pervades math, appearing seemingly from nowhere in a vast number of important equations. It is approximately 2.71828….
  • The number i, defined as the square root of negative one: √(-1). The most fundamental of the imaginary numbers, so called because, in reality, no number can be multiplied by itself to produce a negative number (and, therefore, negative numbers have no real square roots). But in math, there are many situations where one is forced to take the square root of a negative. The letter i is therefore used as a sort of stand-in to mark places where this was done.
The properties and thinking behind the equation are used in quantum mechanics and the design of circuits that use alternating current (a common practice in electrical engineering). Additionally, complex numbers (and their cousins, the hyper complex numbers) have a property that makes them especially useful for studying computer graphics, robotics, navigation, flight dynamics, and orbital mechanics: multiplying them together causes them to rotate.
https://www.livescience.com/51399-eulers-identity.html
 

Knobby22

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Yea, the square root of negative 1 is surprisingly useful in engineering.
You see you have real power which is used and imaginary power at 90 degrees to real power that just moves around.

So for instant a transformer is rated in KVA which means it can handle a total load of real power and not useful current.

Or a generator is rated at 1000kVA and can effectively supply 800kW at 0.8 lagging pf.

It's most used for AC transmission which I did at Uni but have mostly forgotten now.
It's invaluable for working out network parameters to ensure stability.
 
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Something to add to your knowledge bank.
The Most Beautiful equation in Maths.
I am surprised I haven't come across this before, particularly since maths was always a favourite subject of mine.

It seems incredible that three apparently unrelated constants should have such a simple relationship between them.
 
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