Welcome to the March edition of the Epsilon Stream Editors' Picks. We love sharing wonderful mathematics with our readers, so for this month we have quite a variety of picks for you.
You might be interested in exploring the mathematically fairest way two people can share something, or you might be curious about patterns related to gears. The free and safe Epsilon Stream App presents you with the best of such videos, and much more -- all about mathematics. You can search the App for almost anything you can think of in the realm of K - 12 mathematics and related exploratory areas. In fact, our content team at One on Epsilon continuously updates the content in Epsilon Stream. We are parents, teachers, curriculum developers and mathematics researchers, and we just love watching and discussing mathematics videos.
Doodling in Math Class: Triangle Party by Vihart: What interesting patterns can you make with triangles? As you will see in this video, there are quite a lot of possibilities -- all sorts of symmetric arrangements that may remind you of different geometries, many types of polygons, and even fractals. We hope that you enjoy this triangle party!
Proof Without Words: The Circle by minutephysics: Imagine that you have a circle of radius R. You know that the circumference of that circle can be calculated using the expression 2 x π x R (this is a defining property of the constant π). But... using this information, you want to derive the formula for the area of this circle. How do you do it? This short video gives a nice visual on one way of thinking about it.
When Gears Mesh Just Right by GoldPlatedGoof: This recently released video starts by investigating the shapes of gears and related patterns. Throughout, we see some exquisite images, animations, and even artwork by Escher. We are then treated to a presentation of some of the mathematics involved. In this case -- transformations, stereographic projections, complex numbers and functions. You will surely be dazzled by the animations and by what you can do with a mathematical perspective.
Visualising Pythagoras: ultimate proofs and crazy contortions by Mathologer: You may have come across the result of Pythagoras' Theorem before, but how do you prove it? This brilliant video takes us through several beautiful proofs of this famous theorem, with a goal of finding the most straightforward one. Along the way, you'll discover some unexpected facts related to the theorem. If you are interested in learning something about Pythagoras' Theorem, then watch this video!
Hyperbolic Geometry: An Introduction by Uncommon Nonsense: This video is a well-thought-out brief introduction to the five Euclidean postulates, and what is meant by non-Euclidean geometry. While the focus is mostly on hyperbolic geometry, there are some broader gems of geometric wisdom in this video. We also used it in our recent One on Epsilon Blog post about geometries.
Order from Chaos by Numberphile: The problem described in this video sounds simple enough, but how many solutions can you make? This video will surely get you thinking!
The Fairest Sharing Sequence Ever by standupmaths: Have you ever thought about how to share things evenly between two people? In this video, Matt Parker introduces the Thue-Morse sequence and explains how it provides insight into the problem of sharing. As Matt outlines several curious properties of this fascinating yet simple sequence, you might find connections with other videos we mention above.
Let us know which of these videos you liked the most. We'd love to hear from you.
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