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/2008.00922

This 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/breakingmath

Merchandise

Ad 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/breakingmath

The 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]

Sofía and Gabriel discuss the question of "how many angles are there in a circle", and visit theorems from Euclid, as well as differential calculus.

This episode is distributed under a CC BY-SA 4.0 license. For more information, visit CreativeCommons.org.

Ways to support the show:

Patreon-Become a monthly supporter at patreon.com/breakingmath

The theme for this episode was written by Elliot Smith.

Music in the ad was Tiny Robot Armies by Quiet Music for Tiny Robots.

[Featuring: Sofía Baca, Gabriel Hesch]

Look at all you phonies out there.

You poseurs.

All of you sheep. Counting 'til infinity. Counting sheep.

*pff*

What if I told you there were more there? Like, ... more than you can count?

But what would a sheeple like you know about more than infinity that you can count?

heh. *pff*

So, like, what does it mean to count til infinity? What does it mean to count more? And, like, where do dimensions fall in all of this?

Ways to support the show:

Patreon-Become a monthly supporter at patreon.com/breakingmath

(Correction: at 12:00, the paradox is actually due to Galileo Galilei)

Distributed under a Creative Commons Attribution-ShareAlike 4.0 International License. For more information, visit CreativeCommons.org

Music used in the The Great Courses ad was Portal by Evan Shaeffer

[Featuring: Sofía Baca, Gabriel Hesch]

As a child, did you ever have a conversation that went as follows:

"When I grow up, I want to have a million cats"

"Well I'm gonna have a billion billion cats"

"Oh yeah? I'm gonna have infinity cats"

"Then I'm gonna have infinity plus one cats"

"That's nothing. I'm gonna have infinity infinity cats"

"I'm gonna have infinity infinity infinity infinity *gasp* infinity so many infinities that there are infinity infinities plus one cats"

What if I told you that you were dabbling in the transfinite ordinal numbers? So what are ordinal numbers? What does "transfinite" mean? And what does it mean to have a number one larger than another infinite number?

[Featuring: Sofía Baca; Diane Baca]

Ways to support the show:

Patreon

Become a monthly supporter at patreon.com/breakingmath

This episode is released under a Creative Commons attribution sharealike 4.0 international license. For more information, go to CreativeCommoms.org

This episode features the song "Buffering" by "Quiet Music for Tiny Robots"

There are a lot of things in the universe, but no matter how you break them down, you will still have far fewer particles than even some of the smaller of what we're calling the 'very large numbers'. Many people have a fascination with these numbers, and perhaps it is because their sheer scale can boggle the mind. So what numbers can be called 'large'? When are they useful? And what is the Ackermann function? All of this and more on this episode of Breaking Math

[Featuring: Sofía Baca; Diane Baca]

Ways to support the show:

Patreon

Become a monthly supporter at patreon.com/breakingmath

Merchandise

Purchase a Math Poster on Tensor Calculus at our facebook store at facebook.com/breakingmathpodcast

Neuroscience is a topic that, in many ways, is in its infancy. The tools that are being used in this field are constantly being honed and reevaluated as our understanding of the brain and mind increase. And it's no surprise: the brain is responsible for the way we interact with the world, and the idea that ideas hone one another is not new to anyone who possesses a mind. But how can the tools that we use to study the brain and the mind be linked? How do the mind and the brain encode one another? And what does Bayes have to do with this? All of this and more on this episode of Breaking Math.

[Featuring: Sofía Baca, Gabriel Hesch; Peter Zeidman]

Patreon

Become a monthly supporter at patreon.com/breakingmath

This episode is distributed under a CC BY-SA 4.0 license. For more information, visit CreativeCommons.org.

Spheres and circles are simple objects. They are objects that are uniformly curved throughout in some way or another. They can also be defined as objects which have a boundary that is uniformly distant from some point, using some definition of distance. Circles and spheres were integral to the study of mathematics at least from the days of Euclid, being the objects generated by tracing the ends of idealized compasses. However, these objects have many wonderful and often surprising mathematical properties. To this point, a circle's circumference divided by its diameter is the mathematical constant pi, which has been a topic of fascination for mathematicians for as long as circles have been considered.

[Featuring Sofía Baca; Meryl Flaherty]

Patreon 

Become a monthly supporter at patreon.com/breakingmath

Join Sofia and Gabriel on this problem episode where we explore "base 3-to-2" — a base system we explored on the last podcast — and how it relates to "base 3/2" from last episode.

[Featuring: Sofía Baca; Gabriel Hesch]