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:
So far, so good. In the past, I have only ever used one method to make spheres. It’s fairly common because it’s really easy and, once you stuff it, it makes for a decent sphere. But… it’s not 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.
Oh. My. I would love to scale this for knitting, too! — as the row gauge for a knit piece will not be the same as the row gauge for a crocheted piece of equivalent stitch gauge. This much I know. The plotting of “X” and “y” axises, however, are just hopelessly vague recollections from long-ago High School Calculus and so I despair of building on your genius…
(but I can’t wait to incorporate the crochet version into this year’s felted xmas decor!)
By: lisab on March 22, 2010
at 12:41 pm
I agree, lisab! It would be great to figure out an ideal sphere in knitting too! Learning to knit is on my to-do list… so maybe someday I will try to figure that one out!
By: mspremiseconclusion on March 22, 2010
at 1:54 pm
I just found you through Ravelry and was so impressed with your sphere! I can’t wait to try one out! Thank you for sharing!
By: Shorty on March 23, 2010
at 1:17 pm
This is wonderful! Here I was thinking that I was the only one who thought the other way of making spheres comes out skewed and not circular at all. I am thinking of making this the base for some spherical patterns. Thank you.
By: Starbeamer on July 2, 2010
at 3:37 pm
Thanks!! I’m glad you like the pattern and I hope it works out with your spherical patterns!
By: mspremiseconclusion on July 3, 2010
at 12:57 pm
There are a couple of knitted perfect spheres. The best-looking one is by Brent Annable, at rav link
http://www.ravelry.com/patterns/library/stockinette-short-row-sphere .
By: sarah-marie on July 3, 2010
at 1:05 pm
hi! um.. i couldnt get the pdf pattern….can u plz post it on ur blog ??
By: tina on August 31, 2010
at 3:36 pm
oh, my! I totally agree… math rules!
I’ll try this pattern today for a baby present I’ll give this afternoon… hope to post something tomorrow…
By: Claudia Micher on September 19, 2010
at 11:43 am
This PDF is amazing! I’m using them to make a molecular structure and they’re coming out beautifully.
Forgive me if this has already been asked/addressed but I didn’t see it brought up – do you have any sort of copyright or ownership restrictions with these patterns? As in, if I want to use some of these with a design, would I be allowed to sell that pattern or items made with the pattern?
By: Vicky on October 18, 2010
at 10:00 am
Thank you thank you thank you for this!
I’ve been using the “tried and true” method, but havealways had trouble getting it to turn out curved without much convincing (and tugging and stretching).
The first time I tried the 20 row pattern, it came out perfectly curved- no finagling required!
[claps hands with glee] ^_^
By: Jennifer Mathis on November 8, 2010
at 3:48 pm
Oh this so rocks! I love you for posting that pdf! I’m trying to make an oddish and the sphere pattern I’ve got for it just turns out nasty. Your spheres are beautiful. I’ve made a Bob-omb, a Voltorb and soon an oddish out of your spheres. When I take a swing at my Despicable Me minion, I might just take one of your spheres and make it a capsule.
With the Voltorb, since he’s two colors I cheated a bit. At the center round I finished off and did the second half using the increases again and simply whip stitched the top and bottom together. It came out lovely.
By: Jeni on January 7, 2011
at 2:00 am
Wow…you are a genius! I’ve always wondered why my spheres came out looking so wonky! Thanks so much!!!
Any way to work out the math for a GIANT sphere? I’ve never seen someone crochet a huge one and I’m wondering how it would go.
By: Curi on February 6, 2011
at 2:53 pm
I would also love to know how to make a gigantic spere! Maybe 10-15 inches diameter?? I’m making an Umbreon for a friend, and want to package it nicely within a big hollow pokeball… any suggestions?
By: Shaun on April 19, 2011
at 12:51 am
Thank you for this pattern!
By: Julia on February 12, 2011
at 8:19 pm
Thanks for the sphere! Math rocks and so do you!
By: Claudia on March 7, 2011
at 1:10 pm
[...] sick at home… It’s a 30 row sphere based on the pattern by Emily which can be found here. Using a 2.5mm hook it ended up slightly bigger than a tennis ball. Tags Categories ball, cat [...]
By: big ball // Kitty Crafts on May 19, 2011
at 9:49 am
hey try saying it as an odf not a pdf because i couldn’t download it because of that.
By: Avery on June 11, 2011
at 3:19 pm
i mean saving.
not saying
By: Avery on June 11, 2011
at 3:20 pm
this is AMAZE-BALLS!! what a beautiful sphere! i do a lot of amigurumi and got tired of being able to see the increases and decreases! i can’t wait to try this pattern
THANK YOU in advance!
By: Scar (@tat2zle) on August 8, 2011
at 1:16 am
This is so cool – the worlds of mathematics and crochet collide. I think this together with your crocheted holy hand grenade make you my new crocheting hero
By: Crochet Geek on September 18, 2011
at 7:13 am
[...] After I threw a little bit of math at it, I came up with a pattern for the number of stitches required in each row to make an ideal sphere! I posted the pattern on my craft blog along with a description of how I solved the problem. [...]
By: A crafty math application « AndtheJoyofDiscovery on October 18, 2011
at 6:51 pm
[...] wanted to share a link to MsPremise’s blog: http://mspremiseconclusion.wordpress.com/2010/03/14/the-ideal-crochet-sphere/ Here she has a pattern that I’ve been using a LOT, and I find it extremely [...]
By: Update: « SomeKindaCritter on November 11, 2011
at 10:19 am
[...] lot of the legwork for this kind of sphere was done by Ms Premise-Conclusion on her blog post: Ideal Crochet Sphere. There she explains her model and compares the standard method to the ideal case. A good read for [...]
By: Wednesday Geek Craft #30: Perfect Crochet Sphere Part 1 « TacoMagic's Random Insanity on November 23, 2011
at 7:32 am
You are my new hero
By: Jennifer Jermasek-John on February 3, 2012
at 5:32 pm
[...] with the theme of “round,” coming in at 72 on my crochet bucket list is this ideal crochet sphere courtesy of the blogger known as Ms. Premise-Conclusion: Ms. Premise-Conclusions ideal crochet [...]
By: Crochetbug » Blog Archive » Going around in (crochet) circles on March 3, 2012
at 11:55 pm
[...] the blog, Ms Premise-Conclusion ,the author shares the following instructions for crocheting an ideal [...]
By: Crocheting a Mathematically Ideal Sphere | Math and Fiber on March 21, 2012
at 6:57 pm
[...] then decrease the same way you increased. But one clever crocheter/mathematician has come up with the PERFECT! sphere! She’s got directions for several sizes – above you can see a ball I crocheted using [...]
By: How To Make 5 Basic Crochet Shapes | moogly on March 26, 2012
at 11:26 am
i’m wordless… awesome! Respect your dedication and patience
By: Hemapriya on March 30, 2012
at 1:48 am
[...] profite de cette balle à grelot pour vous donner deux liens. Le premier vers le tuto de la sphère parfaite, par Ms Premise-Conclusion ( la mienne manque de bourrage, mais elle est belle et bien [...]
By: Greli grelot « toutenmemetemps on May 4, 2012
at 1:21 am
Thanks so much for the pattern! I made some Dragon Ball Z balls with it… http://queenoftheplushies.blogspot.co.nz/2012/05/dragon-balls.html
Love love LOVE your work
By: Erin on May 13, 2012
at 2:05 am
thanks !!!
By: plouf_le_loup on May 29, 2012
at 10:42 am
Thank you for your pattern. New to this. What does Row 10) 4 scdec.mean?
By: Ellen on June 9, 2012
at 4:54 am
Hi! 4 ScDec means Single-Crochet-Decrease the next two stitches together. Repeat this four times.
By: mspremiseconclusion on June 26, 2012
at 10:11 am
I feel terribly dense admitting this but I’m having the worst trouble trying to understand the pattern for the 12 row sphere. Once I hit row 3 I became befuddled. Could someone clarify what it means? Just the structure of the instructions. For instance, when it says “1, inc, 2, Inc, 1, inc, 2, inc, 1″, does that mean increase once, sc twice, inc? Sorry, I am quite new to crocheting.
By: S on June 25, 2012
at 10:25 pm
Hi! Check out the top of the pattern for a break down of the lingo. “Inc” means “2 Sc in next stitch”. “1, inc, 2, inc, 1, inc, 2, inc, 1″ means “Sc in next stitch, Inc, Sc in next 2 stitches, Inc, Sc in next stitch, Inc, Sc in next 2 stitches, Inc, Sc in next stitch”.
Hope this helps!
By: mspremiseconclusion on June 26, 2012
at 10:14 am
Oh thank you so much!
on with my pokéball 
By: S on June 26, 2012
at 7:55 pm
Hi
I have a problem, I don’t understand if I have in row 9, 12 stitches and I do 4scdec as you explained, I don’t understand what to do with the final stitches , could you please explain what this: “Weave loose end through each stitch in the opening” means exactly. Thanks.
By: Crochetingclub Blogspot on July 3, 2012
at 2:35 pm
I think you’re looking at the final row of one of the spheres? When I say ’4 ScDec’ it just means to ScDec 4 times. This will not use up all of the stitches from the previous row, but that’s ok. With the loose end of the yarn, weave it through each of the last 4 ScDec stitches and pull the yarn to close the opening.
Hope this helps!
By: mspremiseconclusion on July 3, 2012
at 3:36 pm
Great, now I understand, Thanks a lot, I going to translate into Spanish if you aloow me to do it. maybe i is translated yet…I don´t Know and many people ask me. Fantastic work
By: Crochetingclub Blogspot on July 3, 2012
at 6:51 pm
[...] serie de patrones (en inglés) con los aumentos precisos por corrida para crear lo que ella llama la esfera de crochet ideal. Toda un geek del [...]
By: Crochet geek | Corriendo con tijeras on July 25, 2012
at 11:59 am
[...] for the face and embroidered the details and attached two safety eyes. The ball pattern is from this blogger who mathematically figured out how to crochet perfect spheres. She’s amazing! I want to [...]
By: Crocheted Love for Cousin-Babies | Craft Zonkey on August 18, 2012
at 12:24 pm
[...] the incredible Darci found this link and shared it with me. It’s about crocheting an ideal sphere. It totally reinforces and [...]
By: I’m the Reason « Nerdy Knitting on August 22, 2012
at 9:51 pm
Today, I went to the beach with my kids. I found a sea shell and gave it to my 4 year old daughter and said “You can hear the ocean if you put this to your ear.” She put the shell to her ear
and screamed. There was a hermit crab inside and it pinched her ear.
She never wants to go back! LoL I know this is completely off topic but I
had to tell someone!
By: central texas dachshund rescue on August 26, 2012
at 4:25 am
Would it be possible to get a bit more info on how to read this pattern? I’m struggling with what the actual numbers mean. For example, does 2, inc, 3, inc mean stitch 1 sc in next 2 chains, then in the next chain, stitch 2 sc into the next stitch, etc…?
By: Joe Bruno (@MrJoeBruno) on September 9, 2012
at 7:24 pm
I do hope you’re receiving comments on this so many years later- I was hoping for more information on using your math to scale the sphere to much bigger proportions, I was hoping for roughly a basketball-sized sphere. Sadly, it’s been many years since I forgot how to do this kind of math. Thanks!
By: Stephanie P. on September 24, 2012
at 5:21 am
OMG, I loved how you used math and crochet! Those are like my 2 favorite things in the world! Lol. Thank you so much for this pattern.
By: Liliana S. Reynoso on October 1, 2012
at 10:11 pm
Hi! I am currently working up your 30 row sphere with super chunky yarn and an N hook… but I was wondering, is there any way I could get you to write up a pattern for a 80 row sphere? I am attempting to make a giant pouf pillow. The 30 row pattern with chunky yard is turning out to be about 12 inches in diameter, but I’d like to make one that is much bigger.
Thanks so much for sharing. My 12 inch sphere is going to make a fun pillow.
By: Karen Brimhall on October 25, 2012
at 6:03 am
[...] be much smaller. OR you can completely adapt the pattern to any size ball you want. I used the Ideal Sphere pattern for mine, and she has a whole slew of sizes you can choose from, I used the 12 [...]
By: Free Pattern – Adventure Time Balls | Rural Rebellion on November 6, 2012
at 12:54 pm
[...] For the pattern for the bunny, I kinda mixed and matched I made a 16 row sphere using this [...]
By: Hello guys! | Of craft and llamas on November 12, 2012
at 11:57 pm
In the pattern, when you say
example: 5, inc, 5 (11) = “Sc in each of next 5 stitches. Inc in next stitch. Sc in each of next 5 stitches. (11 stitches in this row).”
I think that should be 12 stitches after increasing
Love your pattern, thanks,
By: Carol on November 16, 2012
at 2:14 pm
I’m working on the 22 row sphere and can’t seem to get passed row 8. 6,inc, II, inc, II, inc, 5 (39) Please help.
By: Shirley on December 24, 2012
at 12:34 am
Hi, Here is the row in regular (non jibbery) language. “Single crochet in the next 6 stitches. 2 single crochet in the next stitch. Single crochet in the next 11 stitches. 2 Single crochet in the next stitch. Single crochet in the next 11 stitches. 2 single crochet in the next stitch. Single crochet in the next 5 stitches”. Hope this helps!
By: mspremiseconclusion on February 6, 2013
at 5:48 pm
Thank you for sharing, my sphere came out great!
I was just wandering how you calculated the ratio between the amount of rows and the maximum amount of sticthes i.e. 22 stitches near sin(pi/2) for a 10 row sphere. Did you use certain height to width ratio for a sc?
By: Jaco on January 9, 2013
at 3:13 am
I think I used roughly a 1:1 ratio for a single crochet stitch.
By: mspremiseconclusion on February 6, 2013
at 5:46 pm
Reading this post sounded like this in my head: ‘Blah, blah, blah, math, blah, blah-de-blah, blah, blah, math, blah.’ I have NO idea what all of the math nonsense means, but I can’t wait to try your pattern! Thanks for figuring it out for those of us who don’t do math!
By: Lynsi Marie Keeble on February 5, 2013
at 4:07 pm
Probably common crochet sence, but these are worked in a spiral, right? No joining? TIA
By: Yelena Gura on February 6, 2013
at 4:17 pm
Yes, that’s correct!
By: mspremiseconclusion on February 6, 2013
at 5:45 pm
Does inc mean increase in the pdf? I am fairly new to crocheting and don’t understand all the lingo yet so if you could give me something like a table of your abbreviations I would be very appreciative.
By: Kayla Klippenes on February 6, 2013
at 4:25 pm
Yup – you’ve got it. The explanations for the abbreviations will be in the pdf near the top.
By: mspremiseconclusion on February 6, 2013
at 5:45 pm
Thanks a bunch!!!! I’m gonna give these a go right away!!!
By: Fiona on February 21, 2013
at 5:49 pm
Just started making amigurumi’s and I did not like the systematical decs that give slight ribs…was about to rethink those…but you’ve done it for us!! Many thanks from a mathematical crocheteer
)
By: Ien on February 22, 2013
at 4:55 pm
Can I Marry you? Ok… Maybe not, but you are officially on my idol list! Math AND crochet, Get OUTTA HERE with that stuff!! I have now pinned you and will be scouring your blog for other useful tidbits! Thank you!
Much Respect! RESPECT!!!
Kitty
By: Kitty on February 25, 2013
at 5:35 pm
Absolutely fantastic. Thank you so much for figuring this out and sharing with the world.
By: ruthgrace on March 8, 2013
at 5:36 pm
[...] these balls I used this pattern for an ideal crochet sphere. Of course I couldn’t resist the math behind this pattern
, [...]
By: The wedding gift | Geek Sisters on March 13, 2013
at 10:56 am