Making a sphere is something that comes up a lot in the realm of crocheting stuff. But how do you make a really good sphere?

This is something that I pondered one day. After a very brief and half-hearted go of it with google, I decided to answer the question myself… by throwing some math at it. How do you create a sphere when you are working in a row-by-row system (like crochet) where all you can alter is the number of stitches per row?

Well I assumed that each row is equal to a fixed polar angle , Δθ, within the sphere. At each θ, the circumference of the circle that is traced out within the sphere is proportional to sin(θ) (this was just a quickie derivation). Below, is a plot of what the circumference (y-axis) looks like for each θ (x-axis). So, to completely recreate this, I would want the number of stitches in each row to scale to fit this plot:

*ideal*. This method has you increase by the same number of stitches every row until you hit the middle bit, where you work rows even for a little while before you start decreasing by the same amount for each row.

Problem: this is what this method looks like when plotted against the ideal case (the blue dots represent the old method):

It’s just not the greatest. So what I did was to figure out what the ideal number of stitches per row would be, given the sin(theta) dependence. Result: I can make an ideal sphere for however number of rows I want. It’s not as clear as the tried and true method and it’s not intuitive, but it makes a nice looking sphere.

Here is a pdf file where I’ve written up the pattern for ideal spheres of different sizes. I haven’t tried all the different sizes out myself (since I would up to my eyeballs in spheres) so they *should* all work out nicely. Let me know if they don’t.

Enjoy!

p.s. Math rules!

**UPDATE**: Here is a link to a newer post where I include the pattern for some even bigger spheres! Embiggen!

***03.25.10 Update: An error has been spotted on the 10 Row Sphere, rows 5 and 7. (Oops – sorry all!) So this mistake has been fixed and the link has been updated.

***03.27.10 Update: Oops#2 located on 16 Row Sphere and is now fixified.