Math and Science Tutor

The best way to learn math is to actually understand it. Research shows that then you learn 9 times better.

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Euler's identity is e^(πi)=-1. Indeed, on an Argand diagram a complex number with argument π radians is -1.

But this also means that πi=ln(-1), and so 2πi=2ln(-1)=ln(1)=0. How is that possible?

We need to remember that we have 2π radians here, which is the same as 0 radians. It is not the plain number 2π. This is what may cause confusion.

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I am delighted to present our new logo. Our tutoring services are upgrading soon!

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In the book "Alive Mathematics" of the famous mathematician Yakov Perelman (chapter 1), the writer talks about what "making a loop" may mean.🤔

He gave 2 scenarios: making a loop around a tree with a squirrel sitting on it, with the squirrel being stationary. In this case, we can tell that we are making a loop based on the fact that we can see the squirrel from different orientations. We can see its head, its tail, and from the side. ⬅️↖️➡️↘️However, what if the squirrel keeps turning towards us, while we are going around the tree? We cannot see the squirrel from all sides - only its head. Does it mean that we did not make a loop? Or it still does, because we are again making a circular motion?🐿️ Think about this, and the answer will be in the comments :)