Crafty Maths question

[IsolaPribby]

So this is for all you maths geeks out there (and I know there are plenty 😉)

I am crocheting a triangular shawl, I started in the middle, so each row makes it longer and deeper. I have nearly finished one ball of yarn, and want to figure out how big it will be once I finish all three of the balls.
I am sure that there must be a formula to work it out. I can see that each ball of yarn will give the same area, but each subsequent area will be longer and thinner.
I'm looking for an answer in rows, so that if the first ball takes 100 rows, the next will be 40, or 35, or whatever.
Can someone help me? I have attached a photo to help.

I think the ratio of area of similar triangles is the ratio of square of their sides. You are creating a similar, bigger triangle with three balls of wool so the area will be 3 times so the sides should then end up √3 times the size you have now (or about 1.73 times.) How that equates to rows. Hmm. Might have to get some graph paper out. I might also be talking garbage on account of how I left school over 30 years ago. Hmm. Intriguing. Do we have any maths whizzes in the area?

@StevenTechMumsnet thank you!

So if one ball gave me 100 rows, 3 balls would give me 173? I think that makes sense!

I think so. Because the "height" of the triangle is proportional to the sides so it should also go up to about 1.73 times it's original size. And the height is the number of rows. I think (scratches head.)

Its not it's. Tsk.

@StevenTechMumsnet

Its not it's. Tsk.

I hadn't noticed, and even if I had I wouldn't have commented, seeing as you have helped me so speedily!

Area of triangle is 0.5xobasexheight
As it is an isosceles triangle that is 0.5xobase^2

Your final triangle will have area 3x0.5xobase^2
That will equal 0.5xnbase^2
So 0.5xnbase2 = 3x0.5xobase2

nbase = sqrt3 x obase

So Steven is correct

The height is 2x the number of rows
So if you have used 100 rows so far then height=200rows
New height is sqrt3x200
Number of rows is (100xsqrt3)/2

I think.

(NB Base and height are the shorter sides, not the hypoteneuse)

Sorry,
New height is sqrt3x200
Number of rows is (200xsqrt3)/2 = 100xsqrt3

So I also agree with Steven on that.

My approach would be -

1. The area of the part you've already completed can be calculated by multiplying the length of the two shorter sides and dividing by two (because the piece you've knitted is essentially a square that has been halved diagonally).

2. You then multiply the area you calculated above by three, to give total area for three balls worth of knitting.

3. Reversing the process in 1) above should give you the length of the shorter sides of the completed shawl.

So, for example if the shorter sides of what you've already knitted are 30cm ...

1. 30 x 30 = 900 sq cm, divided by 2 is 450 sq cm (area of what you've knitted with one ball)
2. 450 x 3 = 1350 sq cm (area of what 3 balls will produce)
3. 1350 x 2 = 2700. Square root of that is approximately 52cm, which is what the shorter sides of the finished shawl will be.

This doesn't help in terms of rows, and could certainly bear scrutiny from a more mathematical brain, but seems to make sense to me!

Bloody love Mumsnet

Thank you everyone!

This made me smile. Wonderful MN.

Crazy You solved it just fine.
I'm glad we all agree.

And this is why children need to study maths in school.
Otherwise how will they know how big their crochet triangle will end up?

The only time I've used Pythagoras theorem in the 50+ years since I left school was to work out how much bunting a friend would need to make to decorate the village hall.

I knew that MN would come good!

Now I just need to finish it, count my rows, and see if it works in practice!