He says he understand tyhe whole thing

Is this ok for my child? My child is 9

Oh my Euler, what happened with this guy??? His voice is perfect, his approach was great.

i studied surveying, i don't recall not once having this theorem in class

Try hawking and Ellis

So why the proof is wrong

Very nice yet missing a line or two explaining how/why this proof is wrong .Apart from a lack of precision this proof looks good.

Do you think this might be a difference between pure and applied maths? In pure, we need rigour to derive other pure results. In applied maths, we need intuition before we can apply it to real-world problems. Nice video

According to Pick's theorem, the area of a point is -1/2 !

Please make more videos, this is awesome.

The original proof of triangulating the polygon is also pretty simple.

Very clever proof love it!

great video

please do make more videos. great video

Sorry mate, just a technicality...at 1:22, why do you count it as 11/2 ? It still becomes 5.5, but that would be unacceptable here in Europe. We first multiple and divide and then do the addition.

The one came here after seeing the video of "3 Blue 1 Brown" 👍👍

Beautiful, but what if the symmetrical is also inside the polygon (in a non convex case) then the flows doesn t cancel out (I guess dividing the polygon into small convex peace works and you can sum the area)

cool.

Does Pick's theorem generalize to the 3D lattice? Seems intuitively obvious that it would work for a prism with an arbitrary polygon on the ends.

This technology is apparent in origami. I have been folding paper for about 9 years now. We use a method called " circle packing" to help make crease patterns for complex models. You first figure out how many flaps the base of the origami will have, and then you translate that information into a bunch of circles on square piece of paper. Fascinating art. Thank you for the video!

Hi,may be it's a good work but unfortunately there are lot of issues to point out here : - The water or melting - ice analogy proof is not wrong at ALL!, why? Simply continue reading ^^ and enjoy. - The original work proving this formula using physical analogy is done by the german mathematician Christian Blatter - 1997 - [ Mathematics Magazine 70(3),200 ] using Thermal-diffusion analogy proof. - In 2018, the article - in Russian - : "Pick's Formula and Melting - Ice" by the russian mathematician Grigory. A. Merzon in the "Kvant" magazine (9), 36-37, 2018. Where he proved Pick's formula using this Melting - Ice analogy which is a variant of the Blatter's former proof, the so-called " wrong proof!! " in this video. - In addition to the published article, G. A. Merzon had done a beautiful video - in Russian - explaining graphically his charming! proof, without forgetting to point out the originality of the german C. Blatter's proof. + Video Title : ПЛОЩАДЬ ФИГУРЫ НА КЛЕТЧАТОЙ БУМАГЕ - ГРИГОРИЙ МЕРЗОН * Link : ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-z7tZf8NpSuQ.html N.B : If someone would like to translate this video into English using subtitles, it would be so great.

*not my account btw* I am strange, the rigorous proofs (the more unique ones the better) really do it for me. I guess you could call me an Abstractist (huh, ig thats a real word; thought I was making it up....I could say my philosophy is abstractrionism ....... auto correct must be off, I know one of those words is made up) In physics I believe fields are "real" and everything containing useable energy or information is just a disturbance in various fields. (So light IS a wave in the EM field and this disturbance shows up in the spacetime field as either a wave or a particle depending on the nature of the disturbance. A neutron is a wave in the gravitational field, as a sharp high amplitude spike it appears mostly as a particle in the spacetime field but everything can act as a wave to some degree) So to me, a "good proof" is as generalized as possible (and obviously rigorous) I don't care if its self contained, if you can bring in some topology or abstract algebra and do away with dependencies (such as euclidean/metric spaces, or uniformity, density, .....) then it applies to more things and as such is a better proof. Take the example shown, obviously any such shape can be divided into triangles and is probably the basis for the proof. But if your "flow" could be interpreted in some abstract way (maybe this is a special case of equally weighted points, maybe there is an abstract concept akin to cross dimensional flux that could define an "weighted area" in any topological space [im guessing you need a metric, but weighted flows could do away with the need for uniformity or density.] So in your special case the "volume" = H "area" (being a "flat" space or mathematical cylinder) but maybe weighted flows would expand somehow describing a (not flat/mathematically cylindrical) surface in 3 space. Idk, random tboughts.

which book it is

really enjoyed the format of this video. Succinct enough to be never boring yet never confusing, and with enough detail "left as an exercise" to give me something to think about. :D

Awesome wrong proof. But your conclusion is even awesomer! Wholeheartedly agree.

Why aren’t we taught this formula in school alongside the other geometry formulas? This seems more useful, no?

You talk too quietly

Rigorous proofs can explain that something *is* true. Proofs like this can explain *why* something is true.

I'm not sure I understood. The formula for the sum of the interior angles of a polygon only takes in consideration angles referred to vertexes. What about points on the sides of the polygon?

So you've tessellated the plane with circles? But if you swap the circles for squares the angle sum formula no longer applies!

Interesting!

Wait, why is this proof wrong?? It is sound to me. Where's the mistake?

Your sound level was a bit quiet on this one

RIP Infinite Series

The key to more women in science and engineering is simple; Hotter teachers

Symmetry Bugger me.

For anyone wondering, I believe the book was R. Wald's book on general relativity

great work!

My favorite proof is even more wrong. It's so wrong that it stuck and helped me to remember the surface area formula of a sphere. "The surface of a sphere is quite easy to derive. (draws a sphere). We are enclosing the sphere with a cube (draws a cube) and project the sphere on the cube's surfaces (draws a circle on one surface). This circles' area is r²π. Because the sum of all projected circles equals the surface of a sphere and because a cube has 4 surfaces (draws circles on the 3 visible surfaces and one on a hidden surface), we get the surface of a sphere equal to 4r²π." "But a cube has 6 sides" "Yes but then the area formula would be wrong."

Great video and a fascinating proof I've never seen before. Also I really miss PBS Infinite Series. There are some really spectacular maths channels on RU-vid but Infinite Series was one of the best for the short time it lasted. At least we still have Space Time.

I don't understand the difference between these proofs, why is one "right" and one "wrong"?

In maths, there are two kinds of valid proofs: One is rigorous, self contained, and covers every argument that could support or shut down the idea. The other is something I'm able to explain to my neighbor's kid across the street. Both are fine for their different situations. In all honesty, I'd say trying to find both kind of proofs for the many ideas in maths would probably make the subject more fun while also being serious when the time is right.

Great!

You looked as if you were speaking in a lower voice around the corner (by the side of some stairs) trying not to be detected by or found by someone who is searching for you.

Решил по Формуле Пика

The video is nice. Your voice is cool. I would like to hear more from you. Take care.

based and wrong-pilled

Wonderfully done! It shows the cleverness and the fun of math!

Perhaps one way to phrase it is, there are proofs that keep us honest, and there are "proofs" that keep us sane

Way to make it rigorous: consider that quantity, of the amount of the water that's inside the polygon early on, which you showed equals I+B/2−1. That water idea can be easily used to show that it's _additive,_ meaning if you break a polygon into two pieces its value is the sum of the values of the pieces. Once you know it's additive, it falls into place like lego bricks. The unit square, by computation, has value 1, so its value is its area. Adding the square to itself tells us rectangles have the right area. Slicing the rectangles in half gives us that the value for right triangles is their area. Slightly more trickily, any non-right triangle is a rectangle minus some right triangles, so we get triangles as well. And any polygon can be broken into triangles.