1 / 7 has an interesting result: the sequence 142857 repeats itself!
At 1 / 142857 this pattern is repeated: 0.000007 000007 000007 …
If you square 1 / 7 you get the series of powers of 2!
(1 / 7)² = 0, 02 04 08 16 … from 128 the numbers overlap!
I don’t know what that’s good for. It’s interesting.
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The simplest method for the quadrature of the circle
Source: unknown
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Fake Light Source
Normally you see the reflection of the hemisphere light on the top of the sphere. The calculation is based on the normals of the mesh.
demo
But if you change the normals randomly, you get the impression of many light sources around the sphere.
The function showNormals() will show you the normal vectors
On a panel, one could very easily simulate the glitter of sunlight effects.
demo
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Surfing in the U.S.A. - fluid simulation
demo
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Back to 19
If you divide the one (1) by 2, then again by 2, then again by 2, etc. and add up the fractions, each shifted one place to the right, the result is a sum of 0.526315… The reciprocal of this goes to : 1.9
Coding Challange!
Write a programme that displays an image in this way.
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May we download the image?
I found it in the net. You can use any image you like for this task.
I should actually give you full marks. You’ve done the job!
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Wish you had been my prof at uni
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Thanks to claude.ai. This is the first approach.
Me: I have an image and would like to display it artistically. Lines run horizontally and when the colour of the pixel it is on changes it moves the line up or down depending on what colour value it has from grey.
Claude: That sounds like an interesting artistic technique for transforming images. Here is a description of how this effect could be realised…
image line art - Mona Lisa
change this line to get a smoother effect:
const diff = 0.25*(gray - prevGray);
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A new star constellation “Mona Lisa”
demo
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Another coincidence of numbers in connection with the 19 + 81
If you write these numbers one below the other
81
19
and look at them crossed you can read
11 and 89
As I said, if you add up the Fibonacci numbers by one digit, the reciprocal value goes to 89
If you write the powers of 11 one below the other, you get the Pascal’s triangle. Attention: from a given size the numbers overlap!
If you add up the numbers in Pascal’s triangle crosswise, you find the Fibonacci numbers!
This is divin perfection to me!
… and another little gimmick. The ratio of the Fibonacci numbers goes towards phi = 1.6180…
16 / 18 is interesting, as it results in 0.888888…
The 0 as a symbol for nothingness or void stands opposite an infinite number of infinities (8)…
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This is the Mandbrot-Set predicted by a neuronal network.
100K Training-units.
2 hidden layers a 10 nodes
The orgin Mandelbrot-Set in blue:
demo
thanks to claude.ai and chatGPT.
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A small insight of the day. I hope there are physicists present.
E = m c²
for c = 3
E = m * 3² = m * 9
E / 9 = m
Division by 9 reflects the number
so E / 9 = 1/EEEEEEEE…
and so
m = 1/EEEEEEEEEEEE…
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CodingCrusader:
for c = 3
Physicists are not going to like this
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