# If you know what it is, I’d appreciate a name if you’ve got it. It’s Euclidean, on a Euclidean fixed grid, rational numbers, BUT physically rotated 45 degrees clockwise.

If you know what it is, I’d appreciate a name if you’ve got it. It’s Euclidean, on a Euclidean fixed grid, rational numbers, BUT physically rotated 45 degrees clockwise.

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‘m going to find the LCD for it all. Can’t be 25. 1*2*3*4*5 = 120 so I’ll use that for now.

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Treat it like natural time segments.
1 day – 1 part
2 day – 3 parts
3 day – 5 parts
4 day – 7 parts
5 day – 9 parts

I wonder what the length of each segment is? ———————–

Length of each period (represented as time)
Oh, nice. ====

Watch what happens when I start folding the distance lengths together:

2/5
2/5 1/5
3/5 1/5 2/15
4/5 4/15 2/15 1/10
1/1 1/3 1/6 1/10 2/25
1/2
1/3 2/3
1/3 1/2 3/4
1/3 1/2 3/5 4/5
1/2
3/2 3/2
3/2 6/5 4/3
1/1
4/5 10/9
18/25
0.72

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Now there OUGHT to be a way to get from18/25 back to that chart.
[I may need 2/5 as well, as 2/5 relative length of a “singe period” to the whole]
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LCD is 300
—–

The common factors are:
1The Greatest Common Factor:
GCF = 1Solution

The factors of 24 are:
1, 2, 3, 4, 6, 8, 12, 24

The factors of 30 are:
1, 2, 3, 5, 6, 10, 15, 30

The factors of 40 are:
1, 2, 4, 5, 8, 10, 20, 40

The factors of 50 are:
1, 2, 5, 10, 25, 50

The factors of 60 are:
1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60

The factors of 80 are:
1, 2, 4, 5, 8, 10, 16, 20, 40, 80

The factors of 100 are:
1, 2, 4, 5, 10, 20, 25, 50, 100

The factors of 120 are:
1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120

The factors of 150 are:
1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 150

The factors of 180 are:
1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180

The factors of 200 are:
1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 200

The factors of 216 are:
1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 108, 216

The factors of 225 are:
1, 3, 5, 9, 15, 25, 45, 75, 225

The factors of 240 are:
1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120, 240

The factors of 300 are:
1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150, 300

The factors of 333 are:
1, 3, 9, 37, 111, 333

The factors of 360 are:
1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, 360

The factors of 400 are:
1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 200, 400

The factors of 450 are:
1, 2, 3, 5, 6, 9, 10, 15, 18, 25, 30, 45, 50, 75, 90, 150, 225, 450

The common factors are:
1

The Greatest Common Factor:
GCF = 1

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333/300, which is from 400/300 / 360/300 – is from the 5 set.
1, 2, 3, and 4 all fell nicely into 1 or 1/2.

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Relationship of 2/5 to 18/25.
lcd: 10/25, 18/25
gcf: 2

5, 9

5-4 = 1
9-4 = 5

1/5

Right. Both came out of a relationship btwn 1 and 5.
(and 2/5 / 18/25 = 5/9 or 90/225 / 162/225 = 125/225)

225 * 32 = 7200. Good “time number”. (and 18/25= 0.72 in decimal so that’ll make it easier on my brain)
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bah, forget 7200. False lead. But:
225 is a “squared triangular number” (225 = (1 + 2 + 3 + 4 + 5)^2 = 1^3 + 2^3 + 3^3 + 4^3 + 5^3)
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Dead end I’m sure but knowing the shape of 18/25 should allow that chart to unfold.

https://oeis.org/A001110
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“There is no cube in this sequence except 0 and 1. – Altug Alkan, Jul 02 2016 “.

Related to:
a(n) is the number of ways to paint the sides of a nonsquare rectangle using at most n colors. Cf. A039623. – Geoffrey Critzer, Jun 18 2014

Oh, here’s a Wikipedia.
https://en.wikipedia.org/wiki/Squared_triangular_number
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(it’s “not quite” as I need to find a bigger “Squared_triangular_number” but It’s the right path)
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“number of orthogonal rectangles in an n X n checkerboard, or rectangles in an n X n array of squares.”
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Oh! It’s the same chart! Just combining things that add up to a whole square. 1 by 1, 2 by 2, 3 by 3, 4 by 4, 5 by 5 are all valid squares.