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# Mathematics

## How An Infinite Hotel Ran Out Of Room

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If there's a hotel with infinite rooms, could it ever be completely full? Could you run out of space to put everyone? The surprising answer is yes -- this is important to know if you're the manager of the Hilbert Hotel.

## Quadratic Formula - Why Do We Complete The Square?

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The quadratic formula is really useful, but its derivation is confusing to many. Like what is the point of "completing the square" anyway? In this video, I show how "completing the square" has a geometric interpretation--you are actually making the areas of two squares equal to each other!

## How many ways are there to prove the Pythagorean theorem?

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What do Euclid, 12-year-old Einstein, and American President James Garfield have in common? They all came up with elegant proofs for the famous Pythagorean theorem, one of the most fundamental rules of geometry and the basis for practical applications like constructing stable buildings and triangulating GPS coordinates. Betty Fei details these three famous proofs.

Lesson by Betty Fei, directed by Nick Hilditch.

## Pythagoras theorem: Basics

By O & U Learn - Youtube.com

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Pythagoras theorem - Who would've thought triangles could be so problematic? Once again, don't worry! We've got your back on this one. Pythagoras theorem fully explained with simple and mildly challenging questions.

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