What is Zeno’s Dichotomy Paradox? - Colm Kelleher
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Mathematical and logical paradoxes are a fascinating and important subject - and they’re not all as easily resolved as Zeno’s! It takes a few minutes to get there, but here’s a great explanation of (arguably) the most famous paradox in all of math and all the craziness it led to.
Infinite elephants, infinite camels, and more!
The video used a clever way of cutting up a square to prove a seemingly difficult math identity. In fact, it’s often possible to use diagrams to help you “see” why a particular theorem or identity is true (Of course it’s still necessary to be able to write down the algebra!). For instance, check out all the different ways of graphically representing the proof of the Pythagorean theorem.
Other Lessons by Colm:
People love eating pizza, but every style of pie has a different consistency. If "New York-style"--thin, flat, and large--is your texture of choice, then you've probably eaten a slice that was as messy as it was delicious. Colm Kelleher outlines the scientific and mathematical properties that make folding a slice the long way the best alternative...to wearing a bib.
Have you ever wondered what color is? In this first installment of a series on light, Colm Kelleher describes the physics behind colors-- why the colors we see are related to the period of motion and the frequency of waves.
There are three types of color receptors in your eye: red, green and blue. But how do we see the amazing kaleidoscope of other colors that make up our world? Colm Kelleher explains how humans can see everything from auburn to aquamarine.
Can we accurately describe light as exclusively a wave or just a particle? Are the two mutually exclusive? In this third part of his series on light and color, Colm Kelleher discusses wave-particle duality and its relationship to how we see light and, therefore, color.
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