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16,637 Views • Nov 12, 2024 • Click to toggle off description
Can you prove that 0,1, and 4900 are the only such solutions to the problem?
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#math #manim #animation #theorem #iteachmath #mathematics ##mathshorts #mathvideo #mtbos #mathematician #squarepyramidal #numbertheory #cannonballproblem #cannonballrun
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Views : 16,637
Genre: Education
License: Standard YouTube License
Uploaded At Nov 12, 2024 ^^
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RYD date created : 2024-11-21T21:12:09.313355Z
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31 Comments
Top Comments of this video!! :3
Definitely worth taking time to understand, so interesting!
6 |
Built a 24 meter high pyramid of cubic sandstone in my backyard just to confirm the math. It checks out.
18 |
I remember watching a numberphile video about this. It is quite interesting.
22 |
Understood nothing but good animated video.
8 |
S( n ) = 1^2 + 2^2 + ... + ( n - 1 )^2 + n^2 =
= n( n + 1 )( 2n + 1 ) ÷ 6
S( 24 ) = 24 × 25 × 49 ÷ 6 =
= 4 × 25 × 49 =
= 100 × 49 =
= 4900 =
= 70^2
👍😁
19 |
Checked by summating works out
1 |
is there such a problem with triangular numbers and using consecutive triangular numbers to form another pyramid?
|
I don't like how you have to split up the squares. Is there a solution for that?
8 |
What do you mean n=24 is the only pyramid you can arrange as a perfect square?
True, when n=24 we get a perfect square of 4900 (70²)
But wat about n= 6 ?
81=1²+2²+3²+4²+5²+6²
A perfect square of 9x9
|
The bottom square has a side length of 25, you said 24
4 |
I love this!!!
The fact that 4900 is the unique square integer equal to a sum of multiple consecutive square integers is essentially the entire reason the exceptional Lie groups E₆, E₇, and E₈ exist. Moreover, the approach using this fun fact about 4900 is the only real way a person has to get their hands on this problem computationally!
7 |
√4900 = 70
So.... 70^2
|
I dont see any cannon ball
|
@pedrocarvalho9273
1 week ago
Numbers are magic.
26 |