Superhero Triangles - Numberphile
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Date: 2022-04-09
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Comments and reviews: 9
Fwiffo
After watching this video, I had a dream where The Moody Blues were on Sesame Street performing a song about perfect numbers with Cookie Monster. The song included some sort of nonsensical visual proof in high dimensions about their properties.
It did not sound much like a Moody Blues song, and Cookie Monster sounded like he had a cold, so he was a particularly unconvincing lead when they did -Nights in White Satin. -
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After watching this video, I had a dream where The Moody Blues were on Sesame Street performing a song about perfect numbers with Cookie Monster. The song included some sort of nonsensical visual proof in high dimensions about their properties.
It did not sound much like a Moody Blues song, and Cookie Monster sounded like he had a cold, so he was a particularly unconvincing lead when they did -Nights in White Satin. -
reply
Bachir
What an interesting video except at 10: 41 proof was running faster when we needed much more time n more explanations how did they found the three first triangle 11: 01 what are a, and c. we have seen that earlier in this video but we love to see the proof step by step coz thats the main thing we are looking for. Thanks.
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What an interesting video except at 10: 41 proof was running faster when we needed much more time n more explanations how did they found the three first triangle 11: 01 what are a, and c. we have seen that earlier in this video but we love to see the proof step by step coz thats the main thing we are looking for. Thanks.
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Therion
I didn't remember Heron formula for calculating triangle area, but i found my notes from high school and voila! Heron's formula is right there! And alongside with it three other formulas using inscribed or circumscribed circle radius or sinus of angle between two sides. Pffff, who needs a height: )
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I didn't remember Heron formula for calculating triangle area, but i found my notes from high school and voila! Heron's formula is right there! And alongside with it three other formulas using inscribed or circumscribed circle radius or sinus of angle between two sides. Pffff, who needs a height: )
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numberphile
Is there any extension of this to 3 (or N) dimensions? Where total edge length is equal to volume or even superDuper triangles where the N-th dimensional -length- equivalent is the same as the (N-1) AND (N-2) etc. So the volume, total area, and edge length would be the same?
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Is there any extension of this to 3 (or N) dimensions? Where total edge length is equal to volume or even superDuper triangles where the N-th dimensional -length- equivalent is the same as the (N-1) AND (N-2) etc. So the volume, total area, and edge length would be the same?
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Chris
Lay the equal sides of two of those superheros, the ones with a common side length of 10, against each other and you get another right angled triangle, 8 15 17. Invert one of them but keep the equal sides together and you get a Grime quadrilateral.
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Lay the equal sides of two of those superheros, the ones with a common side length of 10, against each other and you get another right angled triangle, 8 15 17. Invert one of them but keep the equal sides together and you get a Grime quadrilateral.
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Jordan
Awesome stuff, I can't believe I've never encountered that triangle formula, it's really nice. Also I wonder if there are any hero triangles which have area = perimeter-2 o_o might be a fun challenge for one of u guys in the comments hehe.
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Awesome stuff, I can't believe I've never encountered that triangle formula, it's really nice. Also I wonder if there are any hero triangles which have area = perimeter-2 o_o might be a fun challenge for one of u guys in the comments hehe.
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Patrick
9: 10
it's quite easy to work out by hand as well since it's the square root of a product and it's an integer.
32 = 2-5
27 = 3-3
which means 32x27x3x2 = 2-6 x 3-4
and then the square root is simply 2-3 x 3-2 = 8x9 = 72
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9: 10
it's quite easy to work out by hand as well since it's the square root of a product and it's an integer.
32 = 2-5
27 = 3-3
which means 32x27x3x2 = 2-6 x 3-4
and then the square root is simply 2-3 x 3-2 = 8x9 = 72
reply
Venkat
What is the use of such triangle. Assembly is easy. Especially the two right angle triangles. Because cutting and pasting is difficult in structures. Maximum metal usage by structure. Surface maths for structure and architecture.
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What is the use of such triangle. Assembly is easy. Especially the two right angle triangles. Because cutting and pasting is difficult in structures. Maximum metal usage by structure. Surface maths for structure and architecture.
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TheDarkWarriorLOLS
Isn't that pair only the unique pair where all sides are relatively prime. Since if we take double of each side length, we get two new ones which are same perimeter (twice of original) and area (four times original.
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Isn't that pair only the unique pair where all sides are relatively prime. Since if we take double of each side length, we get two new ones which are same perimeter (twice of original) and area (four times original.
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