Craftster Community

CROCHET => Crochet: Completed Projects => Topic started by: MsPremiseConclusion on March 14, 2010 01:59:55 PM



Title: Ideal Crochet Sphere (Mathematically!) with pattern
Post by: 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!  ;)

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.


Title: Re: Ideal Crochet Sphere (Mathematically!) with pattern
Post by: kriminie 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!!


Title: Re: Ideal Crochet Sphere (Mathematically!) with pattern
Post by: Slingmomma 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!


Title: Re: Ideal Crochet Sphere (Mathematically!) with pattern
Post by: TroubleT 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. :D


Title: Re: Ideal Crochet Sphere (Mathematically!) with pattern
Post by: Angry Angel on March 14, 2010 02:46:29 PM
Interesting experiment! They do look very neat.


Title: Re: Ideal Crochet Sphere (Mathematically!) with pattern
Post by: ninjanator on March 14, 2010 02:51:59 PM
you rock so much! :) this sphere looks perfect.


Title: Re: Ideal Crochet Sphere (Mathematically!) with pattern
Post by: craftADDchick on March 14, 2010 03:44:17 PM
Most excellent! And Yay For Math! Especially on Pi Day ;)

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 ;D


Title: Re: Ideal Crochet Sphere (Mathematically!) with pattern
Post by: zombiecakeses on March 14, 2010 04:17:14 PM
Fabulously geeky! I love it! :D

This rocks!


Title: Re: Ideal Crochet Sphere (Mathematically!) with pattern
Post by: goldfishpollywog 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*


Title: Re: Ideal Crochet Sphere (Mathematically!) with pattern
Post by: macgillie 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.


Title: Re: Ideal Crochet Sphere (Mathematically!) with pattern
Post by: InvisibleCastle on March 14, 2010 11:09:16 PM
kudos to your math and to your excellent spheres!


Title: Re: Ideal Crochet Sphere (Mathematically!) with pattern
Post by: Retro_Rose on March 14, 2010 11:17:14 PM
Geniuses like you make the crochet world go round!

Get it! :D haha!

Now lets see what your math-itude can do for a pyramid or a cone even!


Title: Re: Ideal Crochet Sphere (Mathematically!) with pattern
Post by: MsPremiseConclusion on March 15, 2010 06:15:30 AM
Thanks everyone!!! I hope it comes in handy for you!

Now, can you figure out the pattern for a perfect circle? I always end up with perfect hexagons ;D

Haha! Don't think I haven't thrown math at this one too! The trouble is, the best way to make a circle is to increase by 6 stitches every row, which means it's always going to look kinda hexagonal. To make it looks more circle-ish, try staggering where your increases are on each row. The more you increase directly on top of the increase from the last row, the more it looks like a hexagon.

Now lets see what your math-itude can do for a pyramid or a cone even!

I haven't tried a cone, but I'm pretty sure if you start with, let's say, 4 stitches in the second ch stitch and then increase by 4 stitches in each row, you should end up with a cone. (At the bottom I would cheat and sew on a separate circle). As for the pyramid...tempting!  :D


Title: Re: Ideal Crochet Sphere (Mathematically!) with pattern
Post by: Maria Merlino on March 15, 2010 06:54:32 AM
Part of Sacred Geometry! Wonderful! Thank you for the patterns!

Maria


Title: Re: Ideal Crochet Sphere (Mathematically!) with pattern
Post by: msface on March 15, 2010 11:14:51 AM
that's awesome! there are a million things a person could do with that. props!


Title: Re: Ideal Crochet Sphere (Mathematically!) with pattern
Post by: craftADDchick on March 15, 2010 12:38:39 PM
Thanks everyone!!! I hope it comes in handy for you!

Now, can you figure out the pattern for a perfect circle? I always end up with perfect hexagons ;D

Haha! Don't think I haven't thrown math at this one too! The trouble is, the best way to make a circle is to increase by 6 stitches every row, which means it's always going to look kinda hexagonal. To make it looks more circle-ish, try staggering where your increases are on each row. The more you increase directly on top of the increase from the last row, the more it looks like a hexagon.


I can't seem to manage the randomness of the increases... That large logical part of my brain just won't allow for it ;) Because they can't be too random, then it'll be lopsided, right? So, my brain wants to force some sort of order onto it, only I haven't made the time to do it...


Title: Re: Ideal Crochet Sphere (Mathematically!) with pattern
Post by: Lunaricyn on March 15, 2010 04:34:30 PM
I love the fact you can't see the increase seam on these. I'll have to start using this for all my amis.


Title: Re: Ideal Crochet Sphere (Mathematically!) with pattern
Post by: Belladune on March 15, 2010 06:02:24 PM
My husband was thoroughly impressed with your perfect crochet...... seriously, he doesn't often say anything unless he's truely impressed. 
They do look like perfect spheres.. I'm going to give it a go, and see if I can replicate your perfectness!


Title: Re: Ideal Crochet Sphere (Mathematically!) with pattern
Post by: azabuey on March 15, 2010 06:28:18 PM
Those are such beautiful spheres!  I used to know math, once upon a time...


Title: Re: Ideal Crochet Sphere (Mathematically!) with pattern
Post by: craftADDchick on March 15, 2010 06:33:21 PM
Since I just came from a gloomy budget forecast meeting for my school district, I'm wondering if I could crochet a few of these perfectly enough to use them as math manipulatives when I teach the geometry unit next year? Guess I need to give it a try ;)


Title: Re: Ideal Crochet Sphere (Mathematically!) with pattern
Post by: kirsa on March 15, 2010 08:14:49 PM
Awesome.  I have been wondering for ages why nobody had attempted a mathematically accurate crocheted sphere (other than the fact that it's complicated).  And now you have done it.  And I shall have to try your pattern for it, at least once, because of its awesomeness.


Title: Re: Ideal Crochet Sphere (Mathematically!) with pattern
Post by: glambastard on March 15, 2010 08:54:51 PM
these are awesome!


Title: Re: Ideal Crochet Sphere (Mathematically!) with pattern
Post by: FairyFemme on March 15, 2010 09:43:23 PM
You are so utterly awesome for posting this pattern!

I was just wondering how I would go about crocheting an ideal spear for one of my pieces.

Love love love!



Title: Re: Ideal Crochet Sphere (Mathematically!) with pattern
Post by: Purpley Goodness on March 16, 2010 12:29:45 AM
This is fantastic!  Do you think the same principle would work for a knitted object, or are knitted stitches too different in dimension to crochet?  (Sorry if it's a dumb question, my maths/knowledge of crochet vs knit stitch dimensions is a little rusty!)  The reason I ask is that my friend loves the Carmen Miranda type orange singing Carmen from Sesame St (got her into a lifetime love of opera, believe it or not!) - here's the youtube link :  http://www.youtube.com/watch?v=jG-0_p_yefg&feature=PlayList&p=0C82DB214157974D&playnext=1&playnext_from=PL&index=8

and I want to knit her her own for her birthday  ;D (can't crochet).  Your input/advice would be much appreciated!
I bow to your awesomeness!


Title: Re: Ideal Crochet Sphere (Mathematically!) with pattern
Post by: MsPremiseConclusion on March 16, 2010 08:13:41 AM
Do you think the same principle would work for a knitted object, or are knitted stitches too different in dimension to crochet? 

Oooo, good question. I, unfortunately, don't know the first thing about how to knit (it's on my to-learn list), but I do know that knitted balls seem to be worked in wedges as opposed to spirals. This would mean you would need a different pattern. (You could try scouting for different methods online, though).
But your singing orange idea sounds adorable!


Title: Re: Ideal Crochet Sphere (Mathematically!) with pattern
Post by: mrsflibble on March 16, 2010 12:16:42 PM
*cries* these are beautiful, thankyou!!!!!


Title: Re: Ideal Crochet Sphere (Mathematically!) with pattern
Post by: Aikibookworm on March 16, 2010 05:20:16 PM
*geek purring*


Title: Re: Ideal Crochet Sphere (Mathematically!) with pattern
Post by: laf1110 on March 17, 2010 08:37:19 AM
Fantastic!  And to think I never thought I would use much math out of school.  My math teacher is probably laughing maniacally  ;D


Title: Re: Ideal Crochet Sphere (Mathematically!) with pattern
Post by: milksmom on March 17, 2010 09:09:40 AM
Those are such beautiful spheres!  I used to know math, once upon a time...
Can't say it better than this ^^^


And we do need to explore the knit version of a mathish sphere. Knit stitches end up being rectangular, but single crochet stitches are fairly square.


Title: Re: Ideal Crochet Sphere (Mathematically!) with pattern
Post by: MizzKodak on March 18, 2010 02:24:36 PM
this looks amazing, I can thing of many to make earrings, necklaces, add-ons to existing clothing, an endless amounts of ideas.


Title: Re: Ideal Crochet Sphere (Mathematically!) with pattern
Post by: danirene on March 21, 2010 12:04:58 PM
That's amazing. I don't crochet, but I do knit, and so this seems pretty much mind-blowing.


Title: Re: Ideal Crochet Sphere (Mathematically!) with pattern
Post by: Ruby Copperhead on March 22, 2010 12:29:06 PM
I am so fascinated that you made these patterns! Congrats, this is so heart warming! Now if I only had the patience to follow through such a long pattern... I wish I could make a whole solar system out of these... although of course I know planets aren't perfect spheres, yeah, you can all shut up ;D but it still would be cool ;D


Title: Re: Ideal Crochet Sphere (Mathematically!) with pattern
Post by: pixelatedmushroom on March 23, 2010 01:17:29 AM
awesome - thanks so much for sharing :)


Title: Re: Ideal Crochet Sphere (Mathematically!) with pattern
Post by: ld on March 25, 2010 10:58:56 PM
This is glorious. Math makes everything better!


Title: Re: Ideal Crochet Sphere (Mathematically!) with pattern
Post by: rogueknitter on March 26, 2010 06:19:30 AM
This is so cool!

So of course the first thing that I thought when I saw it was that if you crochet it in grey yarn, it would look just like the big sphere in Epcot!  (Can ya tell I need a vacation!!??!)


Title: Re: Ideal Crochet Sphere (Mathematically!) with pattern
Post by: ragdoll193 on March 30, 2010 09:46:05 PM
i made the 14 row sphere tonight, but how do you do your decreases? they appear much less lumpy than mine


Title: Re: Ideal Crochet Sphere (Mathematically!) with pattern
Post by: tidesong on March 31, 2010 08:26:17 AM
Wow, this is quite some math! I have to try it sometime :) Thanks for the pattern!


Title: Re: Ideal Crochet Sphere (Mathematically!) with pattern
Post by: MsPremiseConclusion on April 01, 2010 11:05:07 AM
Thanks again for the great comments everyone!

i made the 14 row sphere tonight, but how do you do your decreases? they appear much less lumpy than mine

I like to do my spheres 'V' side/right side out, and I use the invisi-single crochet decrease stitch, which only works when your piece is 'V' side/right side out. (You do a regular ScDec stitch, but you only use the front loops.) If you want to take a look, I explain it on my blog: http://mspremiseconclusion.wordpress.com/2010/03/23/invisi-single-crochet-decrease/

I am so fascinated that you made these patterns! Congrats, this is so heart warming! Now if I only had the patience to follow through such a long pattern... I wish I could make a whole solar system out of these... although of course I know planets aren't perfect spheres, yeah, you can all shut up ;D but it still would be cool ;D

A Solar System would be SO COOL! (Don't think I havent thought about doing it too!)  :D


Title: Re: Ideal Crochet Sphere (Mathematically!) with pattern
Post by: ragdoll193 on April 01, 2010 03:55:23 PM
ooohhhh... that makes sense! I usually forget that you can use just one loop, since that is what made me not know how to crochet properly originally!


Title: Re: Ideal Crochet Sphere (Mathematically!) with pattern
Post by: hopes on April 04, 2010 08:18:15 PM
thanks for sharing, I am going to give it a try!


Title: Re: Ideal Crochet Sphere (Mathematically!) with pattern
Post by: little me on April 05, 2010 09:29:37 AM
Very nice, I will have to give this a try. Thanks for sharing.


Title: Re: Ideal Crochet Sphere (Mathematically!) with pattern
Post by: decembergrace on May 31, 2010 06:08:50 AM
Nice, basic tutorial. Thanks!


Title: Re: Ideal Crochet Sphere (Mathematically!) with pattern
Post by: Ibbigale on May 31, 2010 09:33:49 AM
wow. your spheres are so spherical! hooray for math!!!


Title: Re: Ideal Crochet Sphere (Mathematically!) with pattern
Post by: Cooksterz on May 31, 2010 11:08:46 PM
Just Loved this spherical pattern!!. You are right, making them on the fly is good, but you can really tell the difference on making this style of Sphere! I put mine in a blog, with photo at:

http://cooksterz.blogspot.com/2010/06/sphere.html

Thank you, and as mentioned, this may become a funky doll or animal, as it "cures" on my desk! ha ::)


Title: Re: Ideal Crochet Sphere (Mathematically!) with pattern
Post by: MsVilja on June 04, 2010 09:34:44 AM
I made a crazily coloured ball for my daughters stroller using your pattern!

Fun little thing to make, compared to the standard round shapes!

http://lh3.ggpht.com/_PDPDjvRcSXI/S8xni8yfatI/AAAAAAAACGA/oqbyFP3MD3A/s640/IMG_1318.JPG (http://lh3.ggpht.com/_PDPDjvRcSXI/S8xni8yfatI/AAAAAAAACGA/oqbyFP3MD3A/s640/IMG_1318.JPG)


Title: Re: Ideal Crochet Sphere (Mathematically!) with pattern
Post by: MsPremiseConclusion on June 04, 2010 11:08:28 AM
Wow, your spheres look fantastic!! I love the way they look when they're all multicoloured.

I'm so, so glad you're enjoying the pattern!


Title: Re: Ideal Crochet Sphere (Mathematically!) with pattern
Post by: Cibo on June 08, 2010 11:48:06 AM
This...this is AWESOME.


Title: Re: Ideal Crochet Sphere (Mathematically!) with pattern
Post by: jcy-works on June 08, 2010 02:00:41 PM
wow so mathematic!


Title: Re: Ideal Crochet Sphere (Mathematically!) with pattern
Post by: bluedisaster on June 23, 2010 07:06:28 PM
Love it!


Title: Re: Ideal Crochet Sphere (Mathematically!) with pattern
Post by: Arryl on June 24, 2010 11:24:22 AM
Perfect!  I've been looking for something like this!  Thanks a lot!