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how to calculate parameter?

F
fred
Fri, Jan 7, 2022 5:08 PM

$fn = 60;
dia = 15;
t_factor = 1.4;
circle(dia);
translate([t_factor * dia, 0, 0])
color("blue")
circle(dia);
translate([-t_factor * dia, 0, 0])
color("green")
circle(dia);

I've not performed any tests on the current t_factor (translate factor) as it's more-or-less a rough eyeball guess. I've forgotten most of my high school trigonometry/geometry (last century) and am not certain that what I knew would help me here.
I'd like to know what formula to use to calculate the x-translation that results in the green and blue circles to split the yellow circle's circumference into quarters. The final objective is to create a shape which when duplicated and rotated will be tiled without gaps.
This is the shape which results from using sqrt(2) as the translation factor. I expect that this is the correct answer, but I only stumbled on it. It's been my experience that sometimes a calculation falls into one of the "standard" references in the world.
Can someone explain the development that would confirm this as the correct calculation?

$fn = 60; dia = 15; t_factor = 1.4; circle(dia); translate([t_factor * dia, 0, 0]) color("blue") circle(dia); translate([-t_factor * dia, 0, 0]) color("green") circle(dia); I've not performed any tests on the current t_factor (translate factor) as it's more-or-less a rough eyeball guess. I've forgotten most of my high school trigonometry/geometry (last century) and am not certain that what I knew would help me here. I'd like to know what formula to use to calculate the x-translation that results in the green and blue circles to split the yellow circle's circumference into quarters. The final objective is to create a shape which when duplicated and rotated will be tiled without gaps. This is the shape which results from using sqrt(2) as the translation factor. I expect that this is the correct answer, but I only stumbled on it. It's been my experience that sometimes a calculation falls into one of the "standard" references in the world. Can someone explain the development that would confirm this as the correct calculation?