#Mathober

[talkingnumbers]

Tangent

Not much of a punchline, more like my favorite factoid about tangent. But I'm out of practice! Give me a minute.

[mathhombre]

Other Options

A bit of doodle doggerel for Mathober Day 7: Skew.

Trying to channel my inner Grant Snider.

[uncertain-noob]

I've been getting into heptagons for the last couple of months, since I saw this.

Its from a mathologer video over on yt. s is such that s^3 -2s^2 -s +1, and its solution falls into the casus irreducibilis ie it can't be expressed precisely without complex numbers, even though its real. 1/r and -r/s are the other two solutions to this cubic. Turns out s : 1 ~ 9 : 4. A guy called fray Ignacio Muñoz in a work called "Manifesto Geometrico" claimed to have a construction of the regular heptgon, using that approximation.

This is a copy of the diagram perceptive Ignacio made, found in a paper called "The 'Geometric Manifesto' of fray Ignacio Muñoz (1684), the Kepler heresy and the heptagonal apses of gothic cathedrals" by Josep Lluis i Ginovart and Cinta Lluis-Teruel. This of course leads a reasonable person to ask what Kepler's heresy was exactly. Kepler thought the heptagon couldn't be constructed, Muñoz thought it could. Later, using Galois theory, it was shown that Kepler was right, that the construction by Muñoz wasn't a regular heptagon, it was just close. Most mysteriously, it appears that in the centuries leading up to the work of Kepler and Muñoz, Arabic authors had access to a work by Archimedes on the heptagon, and we have a sort of telephone version of a copy of a copy of a copy of a diagram found therein.

It seems likely that Achimedes was aware of the 9:4 approximation then, but without the text itself, who can say? Hopefully it will be uncovered in some monasteries' library. And who knows what Euclid knew? Anyway, I'm interested in working out better approximations of s and r, or rather, I'm interested in proving some stuff mentioned in "Sections beyond Golden" by Peter Steinbeck. ps Strongly recommend the mathologer channel on yt, lots of interesting stuff.

[hombrepolitico]

There's an October drawing challenge for math called #mathober, and when this image came to me for the theme hole.

[thesoundofsanfranciscorpg]

[mainul1988-blog]

Search engine optimization (SEO) is the art and science of driving targeted website traffic to your website from search engines.

[majoyosei]

[#Gift] Victorian Couple

Another drawing to remember 🥺

They are Piero Fuyumoe and Faty Mathob, old OCs of one of my childhood best friends 💜💙

Today is her birthday and I wanted to draw them as a memory of the old days in which she came to my house to draw with me and we created stories together 🥰

I love you my precious nee and I hope you like this little present, Piero and Faty always will live in my heart, just like you, Happy Birthday!!! 🎉🎂🥳

Without more to say, I hope you like it!! 🍰

[embroiderygang]

Semana 1

¡Hazlo como niña!

Mathob

[mathhombre]

Weak Topology

A topological space is a set with a set of subsets, where the set of subsets is the topology. A topology is weaker or coarser than another topology if it is a subset. The weak topology is the weakest topology on a vector space so that the set of linear functions on the vector space is continuous.

This is a not accurate visualization, but it's what's in my head.

finer/stronger/bigger vs coarser/weaker/smaller

Mathober Day 6: Weak

My colleague Steven Schlicker has a fine, free undergraduate topology text. Great collections of problems. I'm so happy to be in a math department that emphasizes OER texts. Our math colleagues are miles ahead of us math ed folks with that.

[talkingnumbers]

Being Flip

Mathober: inverted

[talkingnumbers]

Perfect Dream

Mathober 21: Perfect

Love the connection between perfect numbers and the Mersenne Primes. But didn't realize I had already used 8128 in a perfect math comic!

[mathhombre]

Superior Quadratic Form

Not sure which way is better. Missed Mathober 4: Form yesterday, so this is make up work.

[talkingnumbers]

Famous Sections

Have you noticed how mathematicians overuse vocabulary? It starts out logically, like cutting up solids with planes, but pretty soon it's all fiber bundles and manifolds.

Dorothy Bernstein was a great US mathematician, first woman president of the MAA, reputed to be a hell of a teacher, but I made up this factoid.

Mathober prompt 4: Section

[talkingnumbers]

Putting It Together

Mathober 5: Integer Partition. The Keyser Söze of math is behind it all.

The Desmos graph for the middle portion. Is this the first time I have a number doing math?

[mathhombre]

Mathematician Detector

Mathober: Potential

It was this or vector field, scalar potential and Jordan Curves.