A certain polyhedron has 6 faces and 8 vertices.

Must it have a hexagonal cross-section?
#iTeachMath #math #WonderWithMe

I'm not stuck. I'm in the middle of all of this wondering, and I just thought you all might like to #WonderWithMe. 4/4

〰️ out with my camera again 〰️

Lab: imstill.developing 🏆

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#filmphotography #filmisalive #35mmfilmphotography #35mmfilm #wonderwithme #wonderaroundsd #sandiego #sandiegophotographer

I use #WonderWithMe to indicate that this is a question I'm still pondering myself, and I do not want it to be spoiled for me, or others. (And I also can't wait until I figure it out to share it with you!) Thus the "limited interaction."

I’m going to continue my practice from The Old Place of using #WonderWithMe to indicate that the question I’m asking is one I’m currently pondering myself, and I DON’T WANT IT SPOILED FOR ME. (I’ll also restrict replies to reinforce the point.) Join me!

#WonderWithMe

Those proportions almost certainly (individually) converge, to approximately 0.4951 (1's), 0.3204 (2's), and 0.1845 (3's).

Are these constants algebraic or transcendental? 🤔

#WonderWithMe

In the text I'm using for Advanced Topics this year, the students are asked to prove that "the curve x²+y²-3=0 has no rational points."

That's cool. And it's easy to picture a circle that has infinitely many rational points.

But can a circle have finitely many rational points?
#WonderWithMe

Red River Gorge in Kentucky.

#RedRiver #RedRiverGorge #Kentucky #StantonKentucky #Hiking #Travel #Camping #WonderWithMe #TravelPhotography #Limestone #Sandstone #Fossils #Waterfalls #NaturalBridges #WonderWithMe #Wanderings #TravelTheGlobe #SladeKentucky

What is the smallest positive integer that can be written as a sum of the squares of two or more consecutive positive integers THREE different ways?

... I answered this question with brute force ( #Mathematica), but I'm wondering if there's a tech-free way to approach it.

#WonderWithMe

Take the binary representation of 1/√2, but then interpret the digits (still all 1s and 0s) in base-3. Clearly this number is also irrational. But is it expressible in some kind of closed form?
#WonderWithMe!

#math #MathSky #iTeachMath
#maths #MathsSky #iTeachMaths

I'm pretty sure the answer is "no," but now I'm wondering how one might prove that. (And I don't want to be told! Thus the "limited interaction." And the #WonderWithMe tag.)

Is there a function f, defined on all nonzero reals, such that
f(f(x))=1/x
?
#WonderWithMe
#iTeachMath

Is it possible to start with a polygon, fold it completely over a single crease, and have the new polygon that its outline forms have a perimeter greater than its original perimeter?
#WonderWithMe #iTeachMath

#WonderWithMe: What if there were a measure of a polygon called "regularity," in which regular polygons had a regularity of 1, and all others had a regularity between 0 and 1. How might this measure be calculated for an arbitrary polygon?

Is it possible for a regular polygon to have two (non-congruent) diagonals that are commensurable?

If so, how?

If not, can you prove it?

#WonderWithMe

Here's 9 consecutive primes that end in a '1':

36539311
36539381
36539401
36539411
36539431
36539441
36539471
36539491
36539501

Are there arbitrarily long runs of consecutive primes that end in a '1'?
#WonderWithMe #iTeachMath #MathSky #math #mathchat

Call a "fan" of chords in a circle a set of chords all sharing a single endpoint, for which all the angles between consecutive chords are congruent.

For a given n, does there exist a circle with a fan of n chords that are all integer-length?

#WonderWithMe