Breaking Math Podcast

Voting systems are, in modern times, essential to the way that large-scale decisions are made. The concept of voicing an opinion to be, hopefully, considered fairly is as ancient and well-established as the human concept of society in general. But, as time goes on, the recent massive influx of voting systems in the last 150 years have shown us that there are as many ways to vote as there are flaws in the way that the vote is tallied. So what problems exist with voting? Are there any intrinsic weaknesses in group decision-making systems? And what can we learn by examining these systems? All of this, and more, on this episode of Breaking Math.Licensed under Creative Commons Attribution-ShareAlike-NonCommercial 4.0 International License. For more information, visit CreativeCommons.org.

Forecasting is a constantly evolving science, and has been applied to complex systems; everything from the weather, to determining what customers might like to buy, and even what governments might rise and fall. John Fuisz is someone who works with this science, and has experience improving the accuracy of forecasting. So how can forecasting be analyzed? What type of events are predictable? And why might Russia think a Missouri senator's race hinges upon North Korea? All of this and more on this episode of Breaking Math.The theme for this episode was written by Elliot Smith.[Featuring: Sofía Baca, Gabriel Hesch; John Fuisz]

In mathematics, nature is a constant driving inspiration; mathematicians are part of nature, so this is natural. A huge part of nature is the idea of things like networks. These are represented by mathematical objects called 'graphs'. Graphs allow us to describe a huge variety of things, such as: the food chain, lineage, plumbing networks, electrical grids, and even friendships. So where did this concept come from? What tools can we use to analyze graphs? And how can you use graph theory to minimize highway tolls? All of this and more on this episode of Breaking Math.Episode distributed under an Creative Commons Attribution-ShareAlike-NonCommercial 4.0 International License. For more information, visit CreativeCommons.org[Featuring: Sofía Baca, Meryl Flaherty]--- This episode is sponsored by · Anchor: The easiest way to make a podcast.  https://anchor.fm/appSupport this podcast: https://anchor.fm/breakingmathpodcast/support

How many piano tuners are there in New York City? How much cheese is there in Delaware? And how can you find out? All of this and more on this problem-episode of Breaking Math.This episode distributed under a Creative Commons Attribution-ShareAlike-Noncommercial 4.0 International License. For more information, visit creativecommons.orgFeaturing theme song and outro by Elliot Smith of Albuquerque.[Featuring: Sofía Baca, Meryl Flaherty]

i^2 = j^2 = k^2 = ijk = -1. This deceptively simple formula, discovered by Irish mathematician William Rowan Hamilton in 1843, led to a revolution in the way 19th century mathematicians and scientists thought about vectors and rotation. This formula, which extends the complex numbers, allows us to talk about certain three-dimensional problems with more ease. So what are quaternions? Where are they still used? And what is inscribed on Broom Bridge? All of this and more on this episode of Breaking Math.This episode is distributed under a CC BY-SA 4.0 license. For more information, visit CreativeCommons.org.The theme for this episode was written by Elliot Smith.[Featuring: Sofía Baca, Meryl Flaherty]

Mathematics is full of all sorts of objects that can be difficult to comprehend. For example, if we take a slip of paper and glue it to itself, we can get a ring. If we turn it a half turn before gluing it to itself, we get what's called a Möbius strip, which has only one side twice the length of the paper. If we glue the edges of the Möbius strip to each other, and make a tube, you'll run into trouble in three dimensions, because the object that this would make is called a Klein flask, and can only exist in four dimensions. So what is a fiber? What can fiber bundles teach us about higher dimensional objects?All of this, and more, on this episode of Breaking Math.[Featuring: Sofía Baca, Meryl Flaherty]

In introductory geometry classes, many of the objects dealt with can be considered 'elementary' in nature; things like tetrahedrons, spheres, cylinders, planes, triangles, lines, and other such concepts are common in these classes. However, we often have the need to describe more complex objects. These objects can often be quite organic, or even abstract in shape, and include things like spirals, flowery shapes, and other curved surfaces. These are often described better by differential geometry as opposed to the more elementary classical geometry. One helpful metric in describing these objects is how they are curved around a certain point. So how is curvature defined mathematically? What is the difference between negative and positive curvature? And what can Gauss' Theorema Egregium teach us about eating pizza?This episode distributed under a Creative Commons Attribution ShareAlike 4.0 International License. For more information, go to creativecommons.orgVisit our sponsor today at Brilliant.org/BreakingMath for 20% off their annual membership! Learn hands-on with Brilliant.[Featuring: Sofía Baca, Meryl Flaherty]

Join Sofía and Gabriel as they talk about Morikawa's recently solved problem, first proposed in 1821 and not solved until last year!Also, if you haven't yet, check out our sponsor The Great Courses at thegreatcoursesplus.com/breakingmath for a free month! Learn basically anything there.The paper featured in this episode can be found at https://arxiv.org/abs/2008.00922This episode is distributed under a Creative Commons Attribution-ShareAlike 4.0 International License. For more information, visit CreativeCommons.org![Featuring: Sofía Baca, Gabriel Hesch]

Join Sofía and Gabriel as they discuss an old but great proof of the irrationality of the square root of two.[Featuring: Sofía Baca, Gabriel Hesch]Patreon-Become a monthly supporter at patreon.com/breakingmathMerchandiseAd contained music track "Buffering" from Quiet Music for Tiny Robots.Distributed under a Creative Commons Attribution-ShareAlike 4.0 International License. For more information, visit creativecommons.org.

If you are there, and I am here, we can measure the distance between us. If we are standing in a room, we can calculate the area of where we're standing; and, if we want, the volume. These are all examples of measures; which, essentially, tell us how much 'stuff' we have. So what is a measure? How are distance, area, and volume related? And how big is the Sierpinski triangle? All of this and more on this episode of Breaking Math.Ways to support the show:Patreon-Become a monthly supporter at patreon.com/breakingmathThe theme for this episode was written by Elliot Smith.Episode used in the ad was Buffering by Quiet Music for Tiny Robots.[Featuring: Sofía Baca; Meryl Flaherty]