Twenty tasks (for crazy, amazing geometry)

3r33556. 3r3-31. 3r? 3539. Warning doctor. 3r33540. Beware of these puzzles. Side effects can include lost afternoons, crumpled hair and exclamations “Aaaaah, here’s how it's done” are so loud that they can crack window glass. 3r3544. 3r33556. 3r3544. 3r33556. A few months ago I stumbled upon a math puzzle on Twitter. Catriona Shearer . They immediately fascinated me: each puzzle is so tangible, handmade, as if asking for it to be solved. And for each you can easily spend an hour of time, or even more. 3r3544. 3r33556. 3r3544. 3r33556. Ekaterin allowed me 3r3r14. hang

you on these puzzles - and shared 20 of their favorite puzzles. She even satisfied my curiosity and admiration by giving an interview (see the end of the article). 3r3544. 3r33556. 3r3544. 3r33556. Enjoy. And do not say that the doctor did not warn. 3r3544. 3r33556.

3r3544. 3r33556. 3r33434. 1. The garden of hours

3r3544. 3r33556. 3r3013. 3r3331. 3r???. 3r3544. 3r33556. 3r3544. 3r33556. 3r? 3539. What part of each circle is painted over? 3r33540. (12 points at an equal distance; the only point inside the circle is its center) 3r-3544. 3r33556. 3r3544. 3r33556. “Unfortunately, out of these six my favorite is the only one that I didn’t think of myself,” Ekaterin says, “is dark blue.” 3r3544. 3r33556. 3r3544. 3r33556. 3r33434. 2. Tipped square

3r3544. 3r33556. 3r3013. trap. 3r3544. 3r33556. 3r3013. 3r3544. 3r33556. 3r3013. 3r388. 3r???. 3r3544. 3r33556. 3r3544. 3r33556. The lengths of the sides of three squares are consecutive integers. 3r? 3539. What is the total area? 3r33540. 3r3544. 3r33556. 3r3544. 3r33556. "I like this one very much: on the basis of it I drew many beautiful patterns." 3r3544. 3r33556. 3r3544. 3r33556. 3r33434. 5. Beautiful haircut

3r3544. 3r33556. 3r3013. What is the area of the blue triangle? 3r33540. 3r3544. 3r33556. 3r3544. 3r33556. “Probably my favorite for all time. Looks just impossible! Here the solution method is called “haircut”, shearing (unfortunately, not in my honor). ” 3r3544. 3r33556. 3r3544. 3r33556. 3r33434. 6. All people are born equal to

3r3544. 3r33556. 3r3013. 3r33130. 3r???. 3r3544. 3r33556. 3r3544. 3r33556. "Another alteration, which I prefer the original." 3r3544. 3r33556. 3r3544. 3r33556. 3r33434. 7. Semicircle Turdaken

3r3544. 3r33556. 3r3013. 3r3145. 3r???. 3r3544. 3r33556. 3r3544. 3r33556. “Puzzles with corners are much harder to make. The students said that it was a rather simple task, but my parents had great difficulties. It seems that this puzzle requires more "knowledge," but the solution process itself is simpler. " 3r3544. 3r33556. 3r3544. 3r33556. 3r33434. 8. Power chords

3r3544. 3r33556. 3r3013. 3r3-3160. 3r???. 3r3544. 3r33556. 3r3544. 3r33556. 3r? 3539. What is the area of the circle? 3r33540. 3r3544. 3r33556. 3r3544. 3r33556. “In school, I did not study the theorem on intersecting chords, so I like to use it everywhere!” 3r-3544. 3r33556. 3r3544. 3r33556. 3r33434. 9. The Tale of Two Circles

3r3544. 3r33556. 3r3013. 3r3181. 3r???. 3r3544. 3r33556. 3r3544. 3r33556. These regular polygons have the same perimeter. Find the ratio of the areas of the inscribed circles. 3r3544. 3r33556. 3r3544. 3r33556. “This is a consequence of another puzzle, but I like it more than the original!” 3r-3544. 3r33556. 3r3544. 3r33556. 3r33434. 10. Doc Oct

3r3544. 3r33556. 3r3013. 3r3544. 3r33556. 3r3013. 3r3544. 3r33556. 3r3013. 3r3544. 3r33556. 3r3013. 3r3544. 3r33556. 3r3013. 3r3544. 3r33556. 3r3013. 3r3544. 3r33556. 3r3013. 3r3544. 3r33556. 3r3013. 3r3544. 3r33556. 3r3013. 3r33381. 3r???. 3r3544. 3r33556. 3r3544. 3r33556. The squares of the same color are the same size. 3r? 3539. What is the area of all shaded areas? 3r33540. 3r3544. 3r33556. 3r3544. 3r33556. "It's quite simple, as soon as you understand - but I didn't understand right away, so the simplicity of the answer surprised me." 3r3544. 3r33556. 3r3544. 3r33556. 3r33434. 20. Tigrogon

3r3544. 3r33556. 3r3013. 3r3402. 3r???. 3r3544. 3r33556. 3r3544. 3r33556. 3r? 3539. What part of the shape is painted over? 3r33540. The hexagon is regular, with evenly spaced points along the perimeter. 3r3544. 3r33556. 3r3544. 3r33556. “I rarely published this. But the picture reminds me of Tigra Tony[с пачек быстрого завтрака Kellogg — прим. пер.]". 3r3544. 3r33556. 3r3544. 3r33556. 3r33418. BONUS:

3r3544. 3r33556. 3r33434. Sunset over the Square City

3r3544. 3r33556. 3r33426. 3r3544. 3r33556. 3r3544. 3r33556. The left square has an area of 4. 3r3-33539. What is the area of the right square? 3r33540. 3r3544. 3r33556. 3r3544. 3r33556. “I like this task, it resembles the sunset over the city of squares.” 3r-3544. 3r33556. 3r3544. 3r33556.

3r3544. 3r33556. If you’ve read this far — perhaps 6 months after you start reading — and your table is surrounded by crumpled papers and empty Chinese food containers, then you will be pleased to read a short interview with Ekaterin. 3r3544. 3r33556. 3r3544. 3r33556. 3r? 3539. How did you come to develop your puzzles? 3r33540. 3r3544. 3r33556. 3r3544. 3r33556. I went on vacation to the Scottish highlands, but forgot to take a coat, so I had to sit in the house alone, while my friends were walking in nature! Nothing remained but to mechanically draw lines on a piece of paper. 3r3544. 3r33556. 3r3544. 3r33556. I didn’t expect it to turn into a hobby, but it is a bit addictive, especially when people send back their decisions that I like. Almost always you can beautifully cut the puzzle that I missed. 3r3544. 3r33556. 3r3544. 3r33556. 3r? 3539. How is the creative process? 3r33540. 3r3544. 3r33556. 3r3544. 3r33556. It all starts with drawing meaningless figures. The result is a whole page of overlapping squares at different angles or regular (type) pentagons with different colored parts, and then I see if there is any good mathematics there — the relationship between lengths or areas or angles. 3r3544. 3r33556. 3r3544. 3r33556. 3r? 3539. Many of your tasks are drawn with a marker on paper. Why such a lutek? 3r33540. 3r3544. 3r33556. 3r3544. 3r33556. I tried to use Desmos and Geogebra, but I didn’t like it very much. In my opinion, it is faster to draw the inscribed circle manually, after a small amount of trial and error, than to beautifully build it in software geometry. 3r3544. 3r33556. 3r3544. 3r33556. In addition, when using the pen, you can invent things, because the lines are so thick. This is a good compromise between looking “right,” but also knowing that you can't just pull out a ruler and measure a shape. 3r3544. 3r33556. 3r3544. 3r33556. One of the nice things about geometry is that it forgives a lot. I can show you a hopeless square or circle, but this is enough to convey a concept because they are so well defined. 3r3544. 3r33556. 3r3544. 3r33556. 3r? 3539. Some of your puzzles give [i] the most 3r3494. minimum information. How do you find this border where the diagram is [i] just 3r3494. defined? 3r33540. 3r3544. 3r33556. 3r3544. 3r33556. Sometimes this minimum is actually a hint, because it sends you along the same road. I prefer to give a little more than necessary, so there are several deceptive routes. It also gives a greater variety of solutions! 3r3544. 3r33556. 3r3544. 3r33556. It was the case, I published a couple of impossible puzzles: fortunately, someone usually points this out pretty quickly! 3r3544. 3r33556. 3r3544. 3r33556. I also published puzzles with a massive amount of unnecessary information, because I did not see a good solution to use only half of the information. 3r3544. 3r33556. 3r3544. 3r33556. 3r? 3539. Tips for potential puzzle makers? 3r33540. 3r3544. 3r33556. 3r3544. 3r33556. Well, here my impostor syndrome will fully manifest. I’m definitely still a newbie - I’ve only been doing this since[статья опубликована в октябре 2018 года — прим. пер.]since august. ! On the other hand, I like to create puzzles and read solutions even more than solve them myself. 3r3544. 3r33556. 3r3544. 3r33556. The main goal of the puzzle should be entertainment - this is what distinguishes it from a standard mathematical task. Thus, you need at least two of the three: 3r3353544. 3r33556. 3r3544. 3r33556. 3r33526. 3r33556. 3r33538. 3r? 3539. Beautiful task setting 3r33540. . Provide a minimum of information so that the reader wonders how this problem can be solved at all. Or a few tantalizing pieces of information, each of which supposedly offers a solution. Regular polygons and circles are fantastic because they hide a huge amount of information. 3r33541. 3r33556. 3r33538. 3r? 3539. Beautiful method 3r33540. . The trick is either the shortest way or a sudden insight that simplifies everything. It may be not the most obvious method. I saw a lot of problems that are solved with the help of algebra or irrational numbers, or terrible expressions with pi, and at the end everything suddenly shrinks - and I understand that there is a simpler way. 3r33541. 3r33556. 3r33538. 3r? 3539. Beautiful answer 3r34040. . It’s not a pleasure to work on a puzzle in order to get an ugly answer at the end. 3r33541. 3r33556. 3r? 3543. 3r3544. 3r33556. Basically, start drawing - find the puzzle that you like to solve, and think about how you can expand or change some of the elements. If you suddenly find relationships that surprise you, then with a high probability they will surprise others. Twitter is a great platform, as people can post their own pictures in response. 3r???. 3r33556. 3r33556. 3r3-3549. ! function (e) {function t (t, n) {if (! (n in e)) {for (var r, a = e.document, i = a.scripts, o = i.length; o-- ;) if (-1! == i[o].src.indexOf (t)) {r = i[o]; break} if (! r) {r = a.createElement ("script"), r.type = "text /jаvascript", r.async =! ? r.defer =! ? r.src = t, r.charset = "UTF-8"; var d = function () {var e = a.getElementsByTagName ("script")[0]; e.parentNode.insertBefore (r, e)}; "[object Opera]" == e.opera? a.addEventListener? a.addEventListener ("DOMContentLoaded", d! ): d ()}}} t ("//mediator.mail.ru/script/2820404/"""_mediator") () (); 3r33550. 3r33556. 3r???. 3r33556. 3r33556. 3r33556. 3r33556.

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