Calculating Material Dimensions for a Semi-Circular Window Rainbow

[CandiAnne]

Hello math wizards!!!!!

I have a half circle window in my home that I'm trying to cut material for to make a rainbow.

Window across is 69"

All blind slats around the arc are 22.25"

At the bottom of the window there is a Center Circle that is 12 tall and 25 width

What length, width and arc would I need to cut each of the 6 pieces of material?

In advance, Thank you SOOOOO MUCH

 

[berkeman]

Welcome to PF.

Could you upload a picture of this window area? I'm having a hard time picturing it from your description. Just use the "Attach files" link below the Edit window to upload a JPEG or PDF copy of your picture. Thanks.

 

[DaveC426913]

This is what we've got so far from your description.

I'm not sure what a blind slat is - I think you are referring to the solid opaque spokes. Presumably, they have a non-zero thickness (unless they really are edge-on metal slats), which will have to be factored in.

There are some other ambiguities:

• Your measurement of the centre half circle's radius (12") and its diameter (25") disagree by a half inch.
• The length of the blind slats (22.25") disagrees with the difference of the semicircles (69"-25"=) 22" by a quarter of an inch.

There are likely all resolved because this is a real world object with non-zero thicknesses (thickneces?) but we'll need a pic and/or more measurements.

 

[berkeman]

This is what we've got so far from your description.

But is that a Plan View or an Elevation View?

 

[DaveC426913]

But is that a Plan View or an Elevation View?

It's a window.


^{Plan view when under construction; elevation view when installed?}

 

[berkeman]

It's a window.


^{Plan view when under construction; elevation view when installed?}

Yup. Which view is your sketch of the window? Is the window the curved piece at the top (Plan View) or are we looking through the window that has a curved top arch (Elevation View)?

 

[DaveC426913]

Yup. Which view is your sketch of the window? Is the window the curved piece at the top (Plan View) or are we looking through the window that has a curved top arch (Elevation View)?

I have read this four six times and I don't understand what you're envisioning.

Do we all agree we are talking about this?

 

[berkeman]

I have read this four times and I don't understand what distinction you're making.

Do we agree we are all talking about this?

View attachment 327237

If your drawing is an Plan View of the window, we are looking down through the roof of the building. The glass would be the curved piece at the top of your drawing.

If your drawing is an Elevation View of the window, we are looking at the wall and the window like we are looking through it to outside, and the window has an arched top.

Hopefully the OP will post a picture soon to clarify...

(Plan View on the left below, and Elevation View on the right):

https://www.google.com/url?sa=i&url...ved=0CBAQjRxqFwoTCLCPyfiznf8CFQAAAAAdAAAAABAE

 

[DaveC426913]

I know what Plans versus Elevations are.
He described it as a window, not a skylight.
What I've drawn is what the OP described.

... we are looking down through the roof of the building. The glass would be the curved piece at the top of your drawing.

I'm not sure why you wouldn't grant that the OP is describing the actual thing (which, incidentally is rainbow-shaped) he wants to make look like a rainbow - rather than something you are inferring.

And I'm still not actually sure how it matters whether the glass is horizontal (plan view) or vertical (elevation view).

 

[Mark44]

I'm not sure what a blind slat is

In a window blind, the slats are the horizontal (or sometimes vertical) thin pieces that rotate through slightly less than 180 degrees to let light in or obstruct its passage through the window.

In your drawing, the 22.25" pieces would be spokes, which is maybe what the OP meant instead of slats. My guess is that the "material" the OP is talking about would be pieces of glass or some kind of plastic in various colors.

At the bottom of the window there is a Center Circle that is 12 tall and 25 width

If the diameter of the circle is 25" its height (radius) would be 12.5".

 

[DaveC426913]

If the diameter of the circle is 25" its height (radius) would be 12.5".

Actually we don't know that. Mathematically, sure. But we do not know that the flat edge of the semi-circle cuts directly through the centre.

This is a semi circle with a diameter of 25" and a radius of 12". (More accurately, it's an arc of about 175 degrees). This is a very real likelihood because of real world objects that have spokes (dotted red line) with non-zero thickness.

We have to go with the OP's measurements (after he double-checks them).

I'll (try to) step back until the OP elaborates.

 

[Mark44]

But we do not know that the flat edge of the semi-circle cuts directly through the centre.

If it's a semicircle, then it's half a circle (described in post #1 as "a half circle window") so the height (a radius) would be half the diameter.

We have to go with the OP's measurements (after he double-checks them).

Based on the name and the avatar image (which obviously aren't conclusive), my best guess is "she."

In any case, the drawing and the photograph don't bear much resemblance to a rainbow, in which the colored sections are more-or-less bounded by concentric circular arcs.

I agree that we need to get a lot more clarification from the OP.

 

[DaveC426913]

If it's a semicircle, then it's half a circle (described in post #1 as "a half circle window") so the height (a radius) would be half the diameter.

Yes. That has been reiterated already, more than once. However, it is also described in post #1 as having a diameter of 25" and a height of 12". That is more specific information than the vague "half circle".

If the "half circle" the OP speaks of is mathematically a 175 degree arc, then both pieces of information can be reconciled.