Category talk:Custom board: Difference between revisions
imported>Cuc (Added a calculation to verify dimensions of board in main article.) |
imported>Cuc |
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A Large has height 1 3/4". If it's lying flat, the isosceles triangle that needs to fit the board has base 1" and height H, where |
A Large has height 1 3/4". If it's lying flat, the isosceles triangle that needs to fit the board has base 1" and height H, where |
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(1) H = ((1 3/4)^2 + (1/2)^2)^(1/2) = 1.82". |
(1) H = ((1 3/4)^2 + (1/2)^2)^(1/2) = 1.82". |
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(3) 2R = (H + (R - x)) = (1.82 + .137) = 1.957" ~ 1 31/32" - rest, with rest < 1/85". |
(3) 2R = (H + (R - x)) = (1.82 + .137) = 1.957" ~ 1 31/32" - rest, with rest < 1/85". |
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[[User:Cuc|Cuc]] ([[User talk:Cuc|talk]]) 17:43, 25 December 2020 (PST) |
[[User:Cuc|Cuc]] ([[User talk:Cuc|talk]]) 17:43, 25 December 2020 (PST) |
Revision as of 01:44, 26 December 2020
Necessary Custom Board Dimensions for Board Makers
To satisfy my curiosity, I'll givev the computation here that confirms that the minimum diameter is 1 31/32" to circumscribe a Large mid. Here's my calculation.
A Large has height 1 3/4". If it's lying flat, the isosceles triangle that needs to fit the board has base 1" and height H, where
(1) H = ((1 3/4)^2 + (1/2)^2)^(1/2) = 1.82".
We can write H = x + R, where R is the radius of the circumscribed circle, and x is the distance from the center of the circle, to the middle of the base. Both x and R are unknown to us. In addition to H = x + R, we get this equation to solve:
(R^2 - x^2) = (1/2)^2, because the base of the Large is still 1/2.
Hence, if we divide this by H = R + x, we are left with R - x, thus
(2) (R - x) = (R^2 - x^2) / (R + x) = (R^2 - x^2) / H = (1/2)^2 / 1.82 = 0.137".
Adding (1) and (2) we find 2R (the diameter of the circle):
(3) 2R = (H + (R - x)) = (1.82 + .137) = 1.957" ~ 1 31/32" - rest, with rest < 1/85".