How good is your geometry? (not bike geometry)

[Speicher]

I would like to find a for use some "scrap" leather, very large quantiies thereof. The pieces are isoceles triangles, with each side measuring 9 inches.

In order to plan different and useful purposes I would like to know:

What is the biggest square that you can cut from the triangle?

Having cut the square out, would the offcuts be "half" the square?

Yes, I could fiddle about with scrap paper, and experiment. But I do not think I have a protractor to make the accurate 60 degree angles that would be needed. Some intelligent person will be able to work out this out very quickly I am sure, not that I need a quick answer, it would just be quicker than me twiddling about with scrap paper.

If the formuala that you use is comparatively simple, I could then use it to calculate the same for different size triangles.

 

[Arch]

Do you mean equilateral triangles? Otherwise, if the 2 sides are 9", what size is the third?

Ah, sorry, you mention 60 degree angles, so it must be equilateral....

hang on...

 

[colly]

Are all sides the same length? Strictly speaking that would be an equilateral triangle.

If it is then off the top of my head I would say that 1/2 the length of the side would give you the length of the side of the square.

What Arch said:Ah, sorry, you mention 60 degree angles, so it must be equilateral....

 

[Arch]

Ok, I've got a bit of paper and a pair of compasses...

I get a square of 4" (I did it to a scale of 1 cm to one inch) and you get one equilateral triangle at the top, 4" each side, and two halves of the same at the bottom, so that's two right angle triangles of 2.5, 4, 5.

How can that be right? I thought a right angle triangle had to be 3, 4, 5...

I'm confused now.

 

[Speicher]

My apologies yes, equilateral triangle.

 

[marinyork]

Why not cut one of the triangles in half and sew each half onto the correct size to make a 9 inch square?

 

[Speicher]

Yes, I could do that. You could join those squares together in a row of say four or six triangles, and then try to add on another row. But with a seam allowance of say half inch, you then end up with not quite a point on each alternate triangle.

It is easier to join squares as much as possible. Yes, that wastes material, but the material would be wasted anyway if no use can be found for it. I was thinking of making bags, using an industrial sewing machine. Small squares would be needed for the "sides" of the bag.

(Long story short) It may not be me making the bags, but people would use the scrap material to make their own.

 

[fossyant]

Are you cat woman ?

 

[Speicher]

No, I am not cat woman.

Just found out about a quantity of scrap leather triangles, and other odd shapes, and trying to work out a use for them, to make something practical and/or decorative. The scrap is in lovely colours, lovely shades of greens, blues etc.

 

[marinyork]

You waste a lot of material as the largest square that can be made is 4.5xcos60 = 4.5(sqrt3)/2 which is around 3.9 inches.

 

[Speicher]

Good point, Marinyork. So using your idea of two triangles, joined to make a square - if items are made that are slightly less than 9 inches in one dimension, the "loss" of the point of the triangle may not be noticed. Rather like when you are tiling a bathroom, the tiles in the corners may not be complete tiles.

Plus, bearing in mind the range of colours, with only slight changes in the shade of that colour, perhaps the "loss" of the point will not show up!

 

[threebikesmcginty]

Haven't you got your SMP book of elementary tables anymore?

Still got mine - all the answers lie within grasshopper!

 

[Speicher]

I might still have a logarithm book somewhere. For the younger peeps on here, that is wot one used before calculators.

 

[marinyork]

Who said I used a calculator?

 

[Speicher]

My apologies, my reference to the calculator was intended for ThreebikesMcginty.

I was impressed with your geometry, thank you. It is many decades since I did geometry and algebra and calculus.