Does this mean that, since division of a length by any positive number is possible using these tools, we can divide the circle into any natural number of equal areas with this method?

oh thats nice.

I think it would have been interesting to explain how you can cut the diameter in 7 pieces using the straight edge and compass, but I really like the conciseness of this video

I think all of the #some2 videos have been great, but there is just something so nice about a short, but elegant video like this

This is brilliant and beautiful! Very nicely done! At first glance, it's not at all obvious how I would divide the diameter into 7 equal segments, but I'll take your word for it that it can be done.

But the real question is: can you also make a NON-regular square?

Very nice! You could alternatively mark points on the radius at distances sqrt(1/7), sqrt(2/7), sqrt(3/7), ... and draw concentric circles, but this method is so much more elegant!

I wish I had seen this when I had a customer who wanted their pizza in 7 slices lmao

But how do you divide a line segment into seven equal parts with a straight edge and a compass? Am I missing something obvious?

After being separated those don't even look like they should fit together to make a circle but the proof is all there, incredible

Although you've spoiled the answer in the video thumbnail, the idea is so brilliant I had to watch it. Thank you for bring this up. I wonder which areas are constructible given a unit area circle, besides the rationals. Wow!

Stay away from my pizza.

I was just thinking of perspective vanishing points in art. That stuff is all about preserving angles. These lines that represent length can be vectors. That being said, any vector can be any unit. So, a perspective vector doesn't have to represent length, it can be anything.

Great visual proof!

My 6 friends are going to love it when I pull this trick out to cut a pizza for us.

The way I'd tackle this problem would be to first construct a line segment with length root 7. From there one would construct concentric circles, one with radius 1 and one with radius root 7. The space between the outer circle and the inner circle can then be divided in six leaving one circle and six arches of equal area.

Beautiful!

Thats actually beautiful

Wow, love the solution 😀 I was always into math/physics, so it’s kinda fun 😉 Hope for more videos and keep up a good work 👍

Amazing. What other regular polygons can we NOT make using the classical tools?

This is beautiful, for years I watch 3blue1brown videos and your videos give me the same vibe. I love it keep up the great videos

Very interesting solution, but by your first few examples, I (incorrectly) assumed the final shape would be a pie piece. Tricky :)

That's gorgeous!

I wish I was shown this when I was in junior high/ high school man, this would have been awesome

This helped me when cutting the pizza for me and my six friends, thank you very much 😊

This needed to be done on IRL paper with the tools mentioned for added effect 😅

Very intriguing! I didn't know it was possible, but you made the problem and proof easy to understand.

Practically works for any number of divisions

Damn those shapes look so cool!

This is really cool

Extremely Satisfying.

This is so cool !!

Mind Blown ! Subscribed

Simple and beautiful.

This demonstration is not limited to 7 sections. I wrote some functions in desmos and both plotted and calculated the areas of m sections where m is a positive integer, and it holds true for any value of m (odd, even, prime, nonprime, etc.) its an interesting bit of work but i don't think its worth saving as a unique file, so if you want to view it yourself, copy and paste the following code into desmos (make sure to limit m to integers by setting step to 1): m=1 a_{1}=\operatorname{round}\left(\frac{2\pi}{m^{2}}\left(\left[1...m ight]^{2}-\left[0...m-1 ight]^{2} ight),4 ight) a_{2}=\operatorname{round}\left(a_{1}\left[\operatorname{length}\left(a_{1} ight)...1 ight],4 ight) a_{3}=\operatorname{round}\left(\left(a_{1}+a_{2} ight),3 ight) A=\sum_{n=1}^{m}a_{3}\left[n ight] c=\frac{\left[1...m ight]}{m} c_{0}=\left[0...m-1 ight] c_{1}=\left[1...m ight] y=\sqrt{c^{2}-\left(x-c ight)^{2}} y=-\sqrt{c^{2}-\left(x+c-2 ight)^{2}} If you want to display some numerical data, copy/paste these three lines in and label them with the following information (desmos doesn't seem to support pasting label, color, or formatting information so I cant just paste it all in one nice block) \left(2c-\frac{1}{m},.05 ight) \left(2c-\frac{1}{m},-.05 ight) \left(2c-\frac{1}{m},-1 ight) {a1} {a2} {a3}

Holy shit..this was a goldmine!

Great Idea!

This was an awesome video! Straight to the point and shows an amazingly simple solution to a complicated problem

woah that is super cool!

This is super interesting and informative, as well as being very intuitive, but I'm more confused about how other regular polygons can be constructed using classical tools but the heptagon cannot lol. Can I get an explanation as to why?

“bro just take a pizza slice like a normal person”

Would've been nice, if mathematical channels forgot the "straigt edge and compass" rule, and remembered that you can use a marked ruler (neusis) too, or a right angle ruler, with wich you can quite easily construct a heptagon.

I'm pretty sure if I could do a pentagon, I could do a heptagon. I can't do either, but you get my point.

Brilliant!

this is so cool thank you.

This is an awesome visual proof

Thanks for another great visual proof.

Your initial examples of dividing the area of the circle into 2, 3, 4, 5 and 6 equally-sized pieces were a bit misleading, since those pieces were also equally-shaped, whereas in your solution for the division into 7 equally-sized pieces the pieces were not equally-shaped but different when compared to each other. So I was a bit confused first and felt a bit mislead about your solution, since I thought you were solving a different problem (= that the pieces should have to be equally-shaped). Is there a solution for the 7-division where the pieces have the same shape too?

POV: ur Voldemort and ur stuck on trying to figure out how to split ur soul into seven pieces for beginners

my six friends gonna hate me next pizza party

Beautiful

(1) In "Edison" it would be possible to create and play Loops in Any Order we like. Example. Loops=(2, 6, 8, 1) or (12, 1, 3, 6.10,) and

Very good - very satisfying.

that is so friggen cool lmao. thanks for making this video!

That was brilliantly beautiful, sir!

Generalized version of the yin and yang

Nice tutorial-5 Bro!

Trisection of an angle next!

Finally, a way to cut pizza for 7-people party

So it's the same concept of a ying-yang shape (where n=2 in that case), but expanding it further. Neat

Subscribed

If you can't make a heptagon using a staight edge and compass, then use a protractor. 360/7=51.42.

nice. A question how do you construct the regular pentagon with a straight edge and compass?

it's a nice trick but I would like to point that, although all seven areas have the same size, they aren't equal. they have different shape.

ngl, I nearly lost it in a good way my mind was blown at the end then I said, "that was so cool"😀🤤

this video is great

great stuff

My approach qould be to just divide 360° into 7, and have each "pizza" slice have that angle. That is one simple way, although the video solution is cool too

Pepsi Logo: *heavy breathing*

Simply beautiful

Nice!

Also, who discovered this gem of a proof?

Wait, but I still don't undestand why a regular heptagon can't be constructed using a straight edge and compass? Where the areas of those 7 sectors not equal?

I'm sorry. But, you fell short on this exercise in math and geometry. Take a closer look. It's fascinating.

cant wait to do this to a pizza

Could you approach the problem by starting with the hexagon method, giving you 6 equal pie slices, and then creating a small circle in the middle which is equal to 1/7 of the area of the whole circle? i.e. Each of the six pie slices gives up a little of its tip to contribute to the inner circle.

Can’t wait to do thos with my next pizza order :D

Next time I get a pizza I will order it cut just like that.

Time to cut my pizza like an absolute madman

now i just gotta wait for an opportunity to show that off, the problem ist that german schools couldn't care less about problem solving

Yin, yang, and uh... yong, yum, yanney, yan, and yern.

Really cool proof, but it relies on a lot of assumptions. I'm only vaguely familiar with compass and straightedge problems, so when you say things like "you can construct 3- to 6-sided shapes but not 7-sided" or "go ahead and divide the diameter into 7 equal parts," I end up needing to take your word for it. Not sure how complicated it would have been to fully illustrate the context and process of this proof, maybe that's outside the scope of the video, but I would have liked to have it

Wow! If it was a logo, I'll be happy!

Did you use manim to do this animation?

I have long wondered about hubcaps with 7 spokes

gonna order a pizza cut like this

Nice sir

Wow!

Bravo!

Is there any modern import to proofs or operations limited to classical tools? Or is it simply a limitation for its own sake (fun)?

But the pie crust allocation is far from equal which could lead to negative outcomes

I wonder if this is how those swirley marbles are made assuming this works with a three dimensional sphere

Interesting. Now i wonder if there's a way so that 7 dwarfs can also simultaneously share the same amount of crust🤔

Hang on, how do you divide up the diameter of the semicircle into 7 equal parts? Edit, I don't know, but I rid realize it's easy to just make a line segment and repeat it 7 times. Find the mind point of the middle one, make a circle from that.

This reminds me of a puzzle.

I found out this idea was extended from constructing Yin-Yang symbol, especially the one used in South Korean flag "Taegeukgi (태극기, 🇰🇷)"! How amazing it is...!

But WHY can't we construct a regular heptagon using a straight edge and compass? Can you prove it can't be done?

Lovely.

Gonna start cutting pizzas like this

All hail the Math Pepsi.