90, 525, 801, 730 Cannon Balls - Numberphile
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EDIT: whoops, Matt just said this at 3: 20, guess I jumped the gun on this one. But nice to know I understand what he's talking about
Date: 2022-04-09
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Comments and reviews: 9
Adam
I found another square cannon ball number: 350644838194527858589696
with the pyramid of 101702017 layers.
I just found another square cannon ball number while I was writing this comment: 3812046491030712720818176
with the pyramid of 225299285 layers.
And another one just before the video finished: 4958487494267756766822400
you can guess the number of layers.
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I found another square cannon ball number: 350644838194527858589696
with the pyramid of 101702017 layers.
I just found another square cannon ball number while I was writing this comment: 3812046491030712720818176
with the pyramid of 225299285 layers.
And another one just before the video finished: 4958487494267756766822400
you can guess the number of layers.
reply
The
So he found only one for square and hexagon, but more than one for octagon?
Sounds like a classic Parker Square of a discovery, tbh.
But to end on a happy note, I propose we call this find the Parker Cannonball Number. He's gotten enough roasting from his Square to last lifetimes, he deserves something be named after him that portrays success instead of failure.
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So he found only one for square and hexagon, but more than one for octagon?
Sounds like a classic Parker Square of a discovery, tbh.
But to end on a happy note, I propose we call this find the Parker Cannonball Number. He's gotten enough roasting from his Square to last lifetimes, he deserves something be named after him that portrays success instead of failure.
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Raghav
I wish I had such a maths teacher, I have fallen in love with maths all over again. Would love to see more such cool stuff from Matt. Also, someone said this isn't a useful number, I think it is - it is fascinating and exciting, such that it pulls you towards math.
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I wish I had such a maths teacher, I have fallen in love with maths all over again. Would love to see more such cool stuff from Matt. Also, someone said this isn't a useful number, I think it is - it is fascinating and exciting, such that it pulls you towards math.
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Jussi
Would there be a tetrahedron that could be arranged as a triangle? They all can be squared as far as I have tried.
And if I pack spheres hexagonally in a round canister, how large does the canister have to be to allow extra spheres around the hexagon?
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Would there be a tetrahedron that could be arranged as a triangle? They all can be squared as far as I have tried.
And if I pack spheres hexagonally in a round canister, how large does the canister have to be to allow extra spheres around the hexagon?
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Ken
Now, what happens when you go up a dimension? Cannonball clusters/volumes? Solid polyhedra made of cannon balls vs a 2D shape made of cannon balls? Mr Matt the 4th dimension Parker, 4 dimensional cannonball volumes vs their 2D counterparts?
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Now, what happens when you go up a dimension? Cannonball clusters/volumes? Solid polyhedra made of cannon balls vs a 2D shape made of cannon balls? Mr Matt the 4th dimension Parker, 4 dimensional cannonball volumes vs their 2D counterparts?
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dustinlovejoy1
That might be useful in an extremely accurate physics simulation where you wanted to simulate squashing a cone into a circle and represent as many points of reference in the simulations transformation of the cone.
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That might be useful in an extremely accurate physics simulation where you wanted to simulate squashing a cone into a circle and represent as many points of reference in the simulations transformation of the cone.
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Kurtlane
Wow, Matt! Great job!
I'm planning to write a book on figurate numbers. I'll put this in and credit you.
Now, what about square pyramids equal cubes? Pentagonal pyramids equal dodecahedrons? Higher dimensions?
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Wow, Matt! Great job!
I'm planning to write a book on figurate numbers. I'll put this in and credit you.
Now, what about square pyramids equal cubes? Pentagonal pyramids equal dodecahedrons? Higher dimensions?
reply
K.
how about numbers that are the same type of polygonal number when they are multiplied by their position in the polygonal sequence. for squares there are infinitely many, but for other polygons?
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how about numbers that are the same type of polygonal number when they are multiplied by their position in the polygonal sequence. for squares there are infinitely many, but for other polygons?
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Sdrawkcab
I broke excel checking the cumulative sums of the first 150, 000 or so square numbers and haven't found anything else that works besides 4900 (other than the questionable answer of 1, lol)
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I broke excel checking the cumulative sums of the first 150, 000 or so square numbers and haven't found anything else that works besides 4900 (other than the questionable answer of 1, lol)
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