The Silver Ratio - Numberphile
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Date: 2022-04-09
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Comments and reviews: 9
Mike
You should point out that there is also the very interesting property that the diagonal of your silver rectangle makes an angle of 22 1/2 degrees with the long side.
Also, you might have noted the series of triangles with one side equal to 1, starting with a square: , 1, 1 sqt 2, (an angle of 45) and going to Japanese rectangle, 1, sqt 2, sqt 3. Then to 1, sqt3, sqt 4 (2) (with an angle of 30 degrees, and then 1, sqt 4, sqt 5, (from which you can construct the golden ratio, and angles like 36 degrees)
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You should point out that there is also the very interesting property that the diagonal of your silver rectangle makes an angle of 22 1/2 degrees with the long side.
Also, you might have noted the series of triangles with one side equal to 1, starting with a square: , 1, 1 sqt 2, (an angle of 45) and going to Japanese rectangle, 1, sqt 2, sqt 3. Then to 1, sqt3, sqt 4 (2) (with an angle of 30 degrees, and then 1, sqt 4, sqt 5, (from which you can construct the golden ratio, and angles like 36 degrees)
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education
MAybe someone more mathematically knowledgeable can explain this to me, but I was curious about what a complex n-bonacci might look like, so I tried working it out. but it just repeats a 12 cycle, ,0, 1, 1+i, i, i, -1+i, -1, -1, -1-i, -i, -i, 1-i, 1, 1, 1+i. This seems odd to me, Could anyone break down me why such a thing would happen, and would this apply to most complex n-bonacci sequences?
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MAybe someone more mathematically knowledgeable can explain this to me, but I was curious about what a complex n-bonacci might look like, so I tried working it out. but it just repeats a 12 cycle, ,0, 1, 1+i, i, i, -1+i, -1, -1, -1-i, -i, -i, 1-i, 1, 1, 1+i. This seems odd to me, Could anyone break down me why such a thing would happen, and would this apply to most complex n-bonacci sequences?
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Adam
Useful, narrative, enthusiasm. This video tells you something about the world, it tells you about a mystery story you have to solve, and the -narrator- of the story tells it with such excitement. This is the ideal case for how to communicate math to the world. Not only have I learned but I'm happier for having done so.
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Useful, narrative, enthusiasm. This video tells you something about the world, it tells you about a mystery story you have to solve, and the -narrator- of the story tells it with such excitement. This is the ideal case for how to communicate math to the world. Not only have I learned but I'm happier for having done so.
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Lawrence
11: 44 There is only approximate equality between this formula and the construction. Remember the construction consists of a sequence of quarter-circles, so the radius only decreases in discrete steps when going to the next quarter-circle, whereas this formula produces a continuously-decreasing radius of curvature.
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11: 44 There is only approximate equality between this formula and the construction. Remember the construction consists of a sequence of quarter-circles, so the radius only decreases in discrete steps when going to the next quarter-circle, whereas this formula produces a continuously-decreasing radius of curvature.
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slkjvlkfsvnls
About the reducing cognitive load thing: that's actually the reason why (I think) people like symmetry. It's actually an idea I came up with today, the same day i watched this video for the first time.
Just to clarify: I don't know if what I said about summary is true, it's just a hypothesis.
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About the reducing cognitive load thing: that's actually the reason why (I think) people like symmetry. It's actually an idea I came up with today, the same day i watched this video for the first time.
Just to clarify: I don't know if what I said about summary is true, it's just a hypothesis.
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Venkat
A square is a surface and the ratios factors are like golden ratio and silver ratio along circular symmetry. Any Fibonacci type is a ratio along circular symmetry line. Half circle. Even geometrical shape like cylinder has a symmetry ratios. Others are cone sphere parabolic cylinder etc.
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A square is a surface and the ratios factors are like golden ratio and silver ratio along circular symmetry. Any Fibonacci type is a ratio along circular symmetry line. Half circle. Even geometrical shape like cylinder has a symmetry ratios. Others are cone sphere parabolic cylinder etc.
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Gustav
there are specific fingernail scissors that are curved so the cut off part doesn't split in three pieces, but you could actually use three file tools and glue them together and use them on one fingernail: D let's just turn it on it's head.
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there are specific fingernail scissors that are curved so the cut off part doesn't split in three pieces, but you could actually use three file tools and glue them together and use them on one fingernail: D let's just turn it on it's head.
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DannyDux
Mathematician: I cut my fingernails by increasing the number of sides until it looks smooth like a circle!
Human\-mathmetician-: I cut my fingernail in a semi-circle shape
Mathematician: But you can't cut half of pi!
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Mathematician: I cut my fingernails by increasing the number of sides until it looks smooth like a circle!
Human\-mathmetician-: I cut my fingernail in a semi-circle shape
Mathematician: But you can't cut half of pi!
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TheAbc45678
At 15: 08 you showed the famous Japanese wave but sadly you didn't indicate which spiral was used in that painting. Was it the Japanese rectangle (or silver ratio) which is mentioned at 9: 09? That would have been nice.
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At 15: 08 you showed the famous Japanese wave but sadly you didn't indicate which spiral was used in that painting. Was it the Japanese rectangle (or silver ratio) which is mentioned at 9: 09? That would have been nice.
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