Jer
@jermath.bsky.social
Permutations today: 52! is 8x10^67. The 7th graders lost it.
December 9, 2025 at 4:29 PM
Permutations today: 52! is 8x10^67. The 7th graders lost it.
I remember figuring this rule out on my own back in high school, where to solve a problem, I needed to know which numbers have an odd number of factors.
December 4, 2025 at 4:54 PM
I remember figuring this rule out on my own back in high school, where to solve a problem, I needed to know which numbers have an odd number of factors.
Thanks for sharing. I was bracing for a challenge, but everything is right there.
November 25, 2025 at 6:03 PM
Thanks for sharing. I was bracing for a challenge, but everything is right there.
So sweet. We had a kitty named Huckleberry who looked a lot this yours many years ago. I'll try and find a photo.
November 23, 2025 at 5:23 PM
So sweet. We had a kitty named Huckleberry who looked a lot this yours many years ago. I'll try and find a photo.
I'd like to say I did that, but I doubled the 27 three times. When I got 216 I realized that would have been easier.
November 10, 2025 at 4:53 PM
I'd like to say I did that, but I doubled the 27 three times. When I got 216 I realized that would have been easier.
Some "let them eat cake" energy going on there
October 31, 2025 at 6:39 PM
Some "let them eat cake" energy going on there
It's funny because it's true.
(Or the least untrue things he's posted.)
(Or the least untrue things he's posted.)
October 29, 2025 at 11:52 PM
It's funny because it's true.
(Or the least untrue things he's posted.)
(Or the least untrue things he's posted.)
I don't think your argument is sound. There's no guarantee that for any P the triangular cross-section can be adjusted by epsilon and intersect all six sides. On a cube-like shape it does, but for my shape it sometimes can't. Does every F=6, V=8 shape have some P that does work?
October 8, 2025 at 6:08 PM
I don't think your argument is sound. There's no guarantee that for any P the triangular cross-section can be adjusted by epsilon and intersect all six sides. On a cube-like shape it does, but for my shape it sometimes can't. Does every F=6, V=8 shape have some P that does work?
Looks like you can get a hexagon. At least for this simple case. www.desmos.com/3d/brrufqrvj4
Desmos | 3D Graphing Calculator
www.desmos.com
October 8, 2025 at 1:53 PM
Looks like you can get a hexagon. At least for this simple case. www.desmos.com/3d/brrufqrvj4
No. A tetrahedron with the tips of two corners sliced off fits the description. I'm having trouble picturing whether it has a hexagonal cross-section.
October 8, 2025 at 1:35 PM
No. A tetrahedron with the tips of two corners sliced off fits the description. I'm having trouble picturing whether it has a hexagonal cross-section.
You guessed correctly. I don't have that one, just the ones that skip by constant amounts.
September 18, 2025 at 3:46 PM
You guessed correctly. I don't have that one, just the ones that skip by constant amounts.
I think I've cracked it. For any even number of people, there are none (I think). For 7, there are 5. For 9, just 3. (I don't know if I'm missing some sporadic cases, though.)
September 17, 2025 at 7:12 PM
I think I've cracked it. For any even number of people, there are none (I think). For 7, there are 5. For 9, just 3. (I don't know if I'm missing some sporadic cases, though.)
Another arrangement is acebd, which is its own dual, matching in the same order: ACEBD.
September 15, 2025 at 4:18 PM
Another arrangement is acebd, which is its own dual, matching in the same order: ACEBD.
Call your arrangement aedbc, and it matches ADBEC after each rotation pictures. The alternate arrangement adbec matches AEDCB. Swap lower-case letters with upper.
September 15, 2025 at 3:36 PM
Call your arrangement aedbc, and it matches ADBEC after each rotation pictures. The alternate arrangement adbec matches AEDCB. Swap lower-case letters with upper.
Desmos | Graphing Calculator
www.desmos.com
September 13, 2025 at 8:06 PM
It seems like the area is not unique. If the triangle is zero the area is 90.25. If it takes up half the square, the isoceles right triangle has area 361(3-2sqrt2) = 61.94. I think there is a missing constraint based on the Pythagoras tag.
September 13, 2025 at 8:01 PM
It seems like the area is not unique. If the triangle is zero the area is 90.25. If it takes up half the square, the isoceles right triangle has area 361(3-2sqrt2) = 61.94. I think there is a missing constraint based on the Pythagoras tag.
The paper doesn't say every shape checked has the property, it only implies no counterexamples had been found. From the paper:
As of today, most of these polyhedra are known to have Rupert’s property, but some remain open.
As of today, most of these polyhedra are known to have Rupert’s property, but some remain open.
August 28, 2025 at 2:20 PM
The paper doesn't say every shape checked has the property, it only implies no counterexamples had been found. From the paper:
As of today, most of these polyhedra are known to have Rupert’s property, but some remain open.
As of today, most of these polyhedra are known to have Rupert’s property, but some remain open.
My damned backwards brain that still mixes up left and right: ∀ is an upside-down "A" bc it's the indefinite article that means there is one, or it exists. ∃ is a backwards E bc it means "for Every."
August 27, 2025 at 12:30 PM
My damned backwards brain that still mixes up left and right: ∀ is an upside-down "A" bc it's the indefinite article that means there is one, or it exists. ∃ is a backwards E bc it means "for Every."
Does $200 worth of groceries fill a whole bag, still?
August 5, 2025 at 4:50 PM
Does $200 worth of groceries fill a whole bag, still?
Spoiler in the graph. www.desmos.com/calculator/y...
Desmos | Graphing Calculator
www.desmos.com
August 3, 2025 at 1:20 AM
Spoiler in the graph. www.desmos.com/calculator/y...
Yes this one is easier. When a=sqrt(3)/3, Area=sqrt(3)/2 - 2/3 www.desmos.com/calculator/a...
Paddy 7/31/25
www.desmos.com
July 31, 2025 at 10:18 PM
Yes this one is easier. When a=sqrt(3)/3, Area=sqrt(3)/2 - 2/3 www.desmos.com/calculator/a...
Area when a=3 is 9/4 - sqrt(3) Not too bad. Work shown in Desmos. www.desmos.com/calculator/6...
Paddy 7/30/25
www.desmos.com
July 31, 2025 at 9:46 PM
Area when a=3 is 9/4 - sqrt(3) Not too bad. Work shown in Desmos. www.desmos.com/calculator/6...
Those are the extremes, but A can be folded to anywhere along BC. The boundary is a smooth curve.
July 22, 2025 at 12:59 AM
Those are the extremes, but A can be folded to anywhere along BC. The boundary is a smooth curve.
Nice one. Here's a Desmos I whipped up. www.desmos.com/calculator/2...
Desmos | Graphing Calculator
www.desmos.com
July 22, 2025 at 12:58 AM
Nice one. Here's a Desmos I whipped up. www.desmos.com/calculator/2...