### Re: how to calculate parameter?

AM
Fri, Jan 7, 2022 5:37 PM

As noted already, sqrt(2) is correct.  But the explanation was a bit
terse.  The reason is that you have a square defined by the radius of the
circle, and the space between the circles needs to be the diagonal of the
square, which is sqrt(2) times the side length.

On Fri, Jan 7, 2022 at 12:09 PM fred via Discuss discuss@lists.openscad.org
wrote:

---------- Forwarded message ----------
From: fred fred_dot_u@yahoo.com
Cc:
Bcc:
Date: Fri, 7 Jan 2022 17:08:44 +0000 (UTC)
Subject: [OpenSCAD] how to calculate parameter?
\$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);

[image: Inline image]

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.

[image: Inline image]
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?

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Cc: fred fred_dot_u@yahoo.com
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Date: Fri, 7 Jan 2022 17:08:44 +0000 (UTC)
Subject: [OpenSCAD] how to calculate parameter?

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F
fred
Fri, Jan 7, 2022 7:44 PM

Your image has cleared everything up. I'm ashamed to consider that I wasn't able to get the synapses firing in the right path to figure that out on my own. In high school, algebraic proofs were fun, now I'm lucky to figure out a = b ... 1 = 2 anymore.
Thanks everyone for the assist.
On Friday, January 7, 2022, 12:37:50 PM EST, Adrian Mariano avm4@cornell.edu wrote:

As noted already, sqrt(2) is correct.  But the explanation was a bit terse.  The reason is that you have a square defined by the radius of the circle, and the space between the circles needs to be the diagonal of the square, which is sqrt(2) times the side length.

On Fri, Jan 7, 2022 at 12:09 PM fred via Discuss discuss@lists.openscad.org wrote:

---------- Forwarded message ----------
From: fred fred_dot_u@yahoo.com
Cc:
Bcc:
Date: Fri, 7 Jan 2022 17:08:44 +0000 (UTC)
Subject: [OpenSCAD] how to calculate parameter?
\$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?

---------- Forwarded message ----------
Cc: fred fred_dot_u@yahoo.com
Bcc:
Date: Fri, 7 Jan 2022 17:08:44 +0000 (UTC)
Subject: [OpenSCAD] how to calculate parameter?