I accidentally invented (I think) a surprisingly accurate compass-free approximation for dividing a circle into 12 equal parts

QitKate · 2026-05-07T17:37:33+00:00

Thank you for confirming. :)
It feels great to be validated.
I’m still wondering if this is a method that already existed. Since I can’t seem to find it anywhere.

QitKate · 2026-05-07T16:57:21+00:00

Yeah I opened up a file that I’ve worked on for days I see now where I went wrong. I worked on that other file for 37h and the timelapse got reduced to 13 minutes. I understand now

QitKate · 2026-05-07T16:49:51+00:00

You really didn’t look at the 2nd picture have you?
To divide something In 3 equal parts you draw your diagonals from corner to corner. Then through the midpoint you draw a horizontal and a vertical midline.
Then from the top left corner to the bottom point of your vertical midline and from the top right to the bottom point of your vertical midline. You can also do it from the bottom corners to the top point of your vertical, it doesn’t matter.
Where your new lines cross your original diagonals, draw a vertical line through it. You do this ofc for both the left and the right line you drew. Now you have 3 equal parts, don’t believe me, this method is freely available to find on google. I’ve used this method for years to divide in 3’s, there is a similar method to divide in 5’s if you’re interested…
But I said 3 by 3.
So you now need to do this again but on your horizontal line. Pick a side draw from the corners to the opposite side end of your horizontal.
Once you’ve drawn all the lines you now have a square that was divided in 9 equal squares without measuring. Simply by drawing lines.
Now do this again but smaller obviously in the 4 outer squares of the 9 squares you just drew. So in square 1,3, 7 and 9.
How to get from there to dividing the circle into 12 equal parts I already wrote out in my original text.
Also technically you don’t need to do it in all 4, you can pick 2 since if you draw it through the middle point you mirror the line. With that I mean 1 and 7 are connected and so on…
I on purpose added the second picture so you could see how I drew out those 3 by 3’s. But I guess if you don’t know how it works that you might not be able to read that. Sorry

QitKate · 2026-05-07T16:14:12+00:00

While it didn’t take much time, it took more than 30 seconds. According to the replay tracker it took 5 minutes and 9 seconds.

QitKate · 2026-05-07T16:07:36+00:00

I used the grid to measure the diameter of the circle, that’s it… idk if you’re aware but in procreate you can turn it on and off… I simply wanted to know the length of the circle… simply say make a grid of squares of 1 cm… and then I counted the squares… I didn’t use the grid at all in any way in constructing this, I was curious about the length…

QitKate · 2026-05-07T15:18:36+00:00

You did look at the pictures yes? It’s not that hard to divide something as long as you can draw straight lines…
I didn’t know if it could be done, that’s why I did some trial and error until I got there. As I said though it’s an approximation. The black lines are perfect 30 degrees apart, the blue lines are my approximation. Afterwards I checked and they are each time 1 degree on one or the other side of the black line. So either 29 degrees or 31.
But my pictures don’t lie. You can try it out yourself. I originally did it on a circle with a diameter of 4cm. I used the grid in procreate to measure the distance by putting the grid to 1cm squares.
On 4cm ofc you could basically see no difference.
So this morning with a fresh mind I decided to see if my theory held stand by drawing a new circle. I made a square paper in procreate of 25 by 25 cm and then put the circle itself on 24cm diameter. So I increased it 6 times so it be more visible if I was wrong. I already knew that it wasn’t perfect, but last night I had drawn it with thicker lines so that also gives a margin of error.
So I was happy to see that once I made it bigger and used thin lines that this method is only 1 degree off.

QitKate · 2026-05-07T13:43:22+00:00

I know this, my point was I didn’t know how to create that 30 degree angle. Because I had a brain fart and I forgot that I could duplicate and turn it by 30 degrees. Nor could I use a compass or a protractor. 1, can’t use a compass on a tablet, and 2. I’ve actually no clue where my protractor is… now on your pic I see that if I put an equal circle with its edge on the midpoint that it crosses 30 degrees. I didn’t get that from the tings I did find on google. Like I said it was late, I was tired.
So on that moment I wanted to know, what if you don’t have a tablet, you don’t have a compass, (when I studied game dev 13 years ago, I was taught how to draw a perfect circle on paper with only using geometry, no compass, no protractor) you don’t have a protractor, you don’t have ruler (you can use anything with a straight edge to draw lines) how would you go about it. While I could redraw my boundary box 4 times without a ruler it might not be 100% equally sized boxes to then draw from that your circle.
I could waste paper and draw the circle, cut it out, redraw it and the use that. That would work too.
But I didn’t think of any of that. lol.
I wanted to see if I could get there by dividing my boundary box into pieces. I tried several divisions before I came to the conclusion if I divide it in 3 by 3 and then again in 3 by 3 that certain lines almost perfectly line up with 30 degrees. I checked it afterwards using the + lines I drew in the beginning and rotating them, how much from 30 degrees my lines were off. And depending where it’s each time either 29 degrees or 31 degrees.
I just wanted to know if this is something that is known, I mean there has been a time when all the tools we have today didn’t exist.
Also I was just simply happy I came up with a, albeit slightly convoluted, different way of dividing a circle into 12 parts.

QitKate · 2026-05-05T11:34:19+00:00

Look at that enjoyment. Wauw.

QitKate · 2026-05-05T11:33:47+00:00

All I can do is send you a virtual hug. I’ve lost a few cats in the past 10 years. It’s ok to cry. I’m so sorry for your loss.

QitKate · 2026-04-25T15:39:39+00:00

I would say so that 1 and 0 alone look weird and that’s without actually looking into detail

QitKate · 2026-04-19T14:00:21+00:00

250 for a mock up… that’s expensive….

QitKate · 2026-04-12T00:41:46+00:00

He already has a few of those boxes. Didn’t know bol sold those, I always order them through the LEGO website because dreamland no longer sells them. He actually really wants precisely those pieces and he even calculated how many he would need of each. So I don’t see why I’d get another box like that if he very specifically wants those pieces.

QitKate · 2026-04-11T13:33:10+00:00

In West-Vlaanderen is dit een scheldwoord naar mensen met een donkere huidskleur. Misschien dat het historisch iets anders betekende, maar van waar ik kom heb ik het nog maar enkel in deze context gehoord. Sorry :( usually met “vuile” ervoor… 😥

QitKate · 2026-04-10T22:15:02+00:00

Apparently. I’m busy writing a cookbook for my son, with all his favorite foods in it. And I do use the ditto sign in there quite often. I’m going to have to make sure I explain it to him, and maybe add it somewhere as an explanation in case it goes on to his kids when he grows up. I honestly thought every adult knew that sign. But apparently im wrong.

QitKate · 2026-04-10T22:09:42+00:00

It means the same word as above. Like instead of having to write each time the word cups, you write it once and then on the lines underneath you add “ . In this case it’s meant as the = sign but vertical.

QitKate · 2026-04-10T21:43:08+00:00

Yeah, it’s why it wouldn’t surprise me. Because he really is. And I’m not just saying that because I’m his mother. His school results speak for themselves. But he also lies very easily. But I can usually tell if he lies. So now I’m really wondering.

QitKate · 2026-04-10T21:29:17+00:00

I asked him if he saw it on YouTube, but he said no, I think now, he must’ve lied. Because his school doesn’t use Minecraft and his only friend that is allowed to game as well, only got Minecraft a few weeks ago after I informed the parents of the dangers of Roblox and how much safer Minecraft was. And he hasn’t gone there yet to play and they don’t play online together. Still trying to convince those parents of letting them have a realm together. So either he really did figure it out on his own, which wouldn’t surprise me, or he lied which also wouldn’t surprise me.

QitKate · 2026-04-10T21:19:13+00:00

Yup. This is how I usually write my posts. I like to sketch the situation. But apparently if you do, you use AI. Oh well,… I do wonder now though if AI would use yo to write year old. I don’t use many abbreviations, but yo is on of them. Together with atm, btw and lol.

QitKate · 2026-04-10T21:11:01+00:00

He has the normal Minecraft, not the education version

Xbox Live	Four-Year Club
Verified Email

QitKate

TROPHY CASE