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Topic: Ideal Crochet Sphere (Mathematically!) with pattern  (Read 73026 times)
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MsPremiseConclusion
« on: March 14, 2010 01:59:55 PM »

Whenever I have to crochet a sphere, I always pull out the tried and true method: increase by the same number of stitches each row for a little while, work the rows even for the middle bit, then decrease by the same number of stitches each row until you're finished.

Once it's stuffed, this makes a decent sphere! Plus, it's a super easy pattern to remember. But it got me to thinking, how would I go about making an ideal sphere?

After I got bored asking google, I threw a little bit of math at it. Turns out the the number of stitches in each row should scale with sin(theta), where theta is the polar angle. (Things I neglected in my quickie model: stretching and spiralling.)

These are two spheres that I made this way:



I included the pattern for the 2 spheres at the end of this post. There are more on my blog, if you are interested.

I found it tricky to figure out how to squeeze a weird number of increases into a row where they in no way fit evenly, so let me know how these patterns work out for you if you try these!

My conclusion for this sphere method: it's really fun and it makes a pretty nice looking sphere, but the tried and true method is just waaay easier!  Wink

Also, math is fun!

The Patterns:

inc = 2 single crochet in next stitch.
dec = single crochet decrease.
These are worked in spiral rounds.

20 Row Sphere:

Row 1) Ch 2. 6 Sc in second Ch from hook. (6)
Row 2) inc in each stitch around. (12)
Row 3) (1, inc) repeat () around (18)
Row 4) 1, inc, 2, inc, 3, inc, 2, inc, 3, inc, 2 (23)
Row 5) inc, 4, inc, 3, inc, 4, inc, 3, inc, 4 (28)
Row 6) 3, inc, 6, inc, 6, inc, 6, inc, 3 (32)
Row 7) 5, inc, 9, inc, 9, inc, 6 (35)
Row 8 ) 3, inc, 10, inc, 11, inc, 8 (38)
Row 9) 12, inc, 25 (39)
Row 10) inc, 38 (40)
Row 11) even
Row 12) 38, dec (39)
Row 13) 25, dec, 12 (38)
Row 14) 8, dec, 11, dec, 10, dec, 3 (35)
Row 15) 6, dec, 9, dec, 9, dec, 5 (32)
Row 16) 3, dec, 6, dec, 6, dec, 6, dec, 3 (28)
Row 17) 4, dec, 3, dec, 4, dec, 3, dec, 4, dec (23)
Row 18) 2, dec, 3, dec, 2, dec, 3, dec, 2, dec, 1 (18)
Row 19) (dec, 1) repeat () around (12)
Row 20) 4 scdec. Fasten off. Weave loose end through each stitch in the opening. Pull tightly to close.

26 Row Sphere:

Row 1) Ch 2. 6 Sc in second Ch from hook. (6)
Row 2) inc in each stitch around. (12)
Row 3) (1, inc) repeat () around (18)
Row 4) 1, inc, 2, inc, 3, inc, 2, inc, 3, inc, 2 (23)
Row 5) 2, inc, 3, inc, 4, inc, 3, inc, 4, inc, 2 (28)
Row 6) 1, inc, 4, inc, 5, inc, 4, inc, 5, inc, 4 (33)
Row 7) 3, inc, 5, inc, 6, inc, 5, inc, 6, inc, 3 (38)
Row 8 ) 8, inc, 9, inc, 8, inc, 9, inc (42)
Row 9) 6, inc, 13, inc, 13, inc, 7 (45)
Row 10) 9, inc, 14, inc, 14, inc, 5 (48)
Row 11) 15, inc, 23, inc, 8 (50)
Row 12) 24, inc, 25 (51)
Row 13) inc, 50 (52)
Row 14) even (52)
Row 15) 50, dec (51)
Row 16) 25, dec, 24 (50)
Row 17) 8, dec, 23, dec, 15 (48)
Row 18) 5, dec, 14, dec, 14, dec, 9 (45)
Row 19) 7, dec, 13, dec, 13, dec, 6 (42)
Row 20) dec, 9, dec, 8, dec, 9, dec, 8 (38)
Row 21) 3, dec, 6, dec, 5, dec, 6, dec, 5, dec, 3 (33)
Row 22) 4, dec, 5, dec, 4, dec, 5, dec, 4, dec, 1 (28)
Row 23) 2, dec, 4, dec, 3, dec, 4, dec, 3, dec, 2 (23)
Row 24) 2, dec, 3, dec, 2, dec, 3, dec, 2, dec, 1 (18)
Row 25) (dec, 1) repeat () around (12)
Row 26)  4 scdec. Fasten off. Weave loose end through each stitch in the opening. Pull tightly to close.
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kriminie
« Reply #1 on: March 14, 2010 02:17:13 PM »

amazing!! i only vaguely remember what sin is but your spheres look amazingly spherey... great job!! my hero!!
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« Reply #2 on: March 14, 2010 02:26:02 PM »

These have to be the best spheres I have ever seen crocheted! I am totally bookmarking this and trying it out for some toys for my son!! Thank you so much for the pattern!
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« Reply #3 on: March 14, 2010 02:43:42 PM »

I love this!

If you made a few other shapes, they would make great gifts for a geometry teacher. Cheesy
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« Reply #4 on: March 14, 2010 02:46:29 PM »

Interesting experiment! They do look very neat.
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ninjanator
« Reply #5 on: March 14, 2010 02:51:59 PM »

you rock so much! Smiley this sphere looks perfect.
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« Reply #6 on: March 14, 2010 03:44:17 PM »

Most excellent! And Yay For Math! Especially on Pi Day Wink

I'm definitely going to make a few of these. Perhaps once I finish my scarf, this can be my Friday Lunch Crochet Group project...

Now, can you figure out the pattern for a perfect circle? I always end up with perfect hexagons Grin
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« Reply #7 on: March 14, 2010 04:17:14 PM »

Fabulously geeky! I love it! Cheesy

This rocks!
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« Reply #8 on: March 14, 2010 07:27:46 PM »

What a perfect post for Pi day!

I look forward to using this in the future.

*bookmarking*
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macgillie
« Reply #9 on: March 14, 2010 08:03:55 PM »

Yea - pi day! These are perfect! I can't even see the increases on the first one.
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