Cool Geometry Challenge

Рет қаралды 63,103

Күн бұрын

Пікірлер: 93

@zxbecollection 10 ай бұрын

Absolutely love your channel Andy. The concise focus on the solution without a lot of tangents (pun intended), and the How Exciting tag-line gets me every time. Keep up the good work!

@theabshow7318 11 ай бұрын

At 3:36, for the denominator you could just use a²-b²=(a+b)(a-b) so that would instantly give you 4²-36×3

@zOni413 11 ай бұрын

Во-первых, он явно знает про эту формулу. Не зря же он решил домножить именно на это число всю дробь. Просто у него в разборах задач он всегда всё делает на максимально доступном уровне, по этому он раскрывал скобки по честному. Во-вторых, у вас опечатка в формуле. P.S. Прошу прощения. Опечатка в формуле появляется только при переводе комментария на русский.

@Pluton1709 11 ай бұрын

i had that in school today thats funny

@theabshow7318 11 ай бұрын

@@zOni413Understood I thought if he told people about that then people would become more efficient in doing problems like that rather than breaking it up which will take up some more time. Generally in entrance tests, people can't afford to lose time in places like that

@invictus8539 11 ай бұрын

He was excited for real this time

@seireiart 10 ай бұрын

yuuka pfp, how exciting

@Randumbvideosss 11 ай бұрын

Hey, Andy I like how you use the 90-60-30 triangle rule but it would be more interesting if you used the sin or cos theta so that one also gets to know how this 30-60-90 came into in the first place.

@normalbattlecat8088 11 ай бұрын

Just bisect an equilateral triangle with side length 2, and you get two 30-60-90 triangles. Take one of said triangles, and notice that the hypotenuse is 2 and the short side is 1. Use pythagorean theorem to get your 1-sqrt3-2 identity

@TheSumitGupta 11 ай бұрын

tan theta

@z000ey 11 ай бұрын

@@normalbattlecat8088 exactly. The a*sqrt(3) doesn't derive from trigonometry but from the Pythagorean theorem.

@Randumbvideosss 11 ай бұрын

@@z000ey huh how? Would you please elaborate?

@z000ey 11 ай бұрын

@Randumbvideosss well if you look at a 30 60 90 triangle and mirror it over the longer cathetus (adjacent) you get a 60 60 60 thus equilateral triangle, thus you know that the shorter cathetus of the original triangle is 1/2 of the hypothenuse and that the longer cathetus of the original triangle is actually the height of the equilateral mirrored one. Using Pythagoras you get hypothenuse c squared equals c/2 squared plus height squared, from which height is (c x sqrt3) /2

@Insightfill 9 ай бұрын

3:09 "Now I want to get x by itself" and ask it to think long and hard about how its life is going, and if it really thinks it's going anywhere in the long-run. Gotta have a plan, x.

@Qermaq 6 ай бұрын

I never want to get my x by itself. I want another responsible adult around just in case things go south.

@gumbspleengle5270 11 ай бұрын

What software do you use for your videos?

@Kreypossukr 11 ай бұрын

I’m also curious about this

@JuanFrancos-kj6vd 10 ай бұрын

Whatever he uses I’m sure it requires a lot of design and planning. What he does is great.

@coolmangame4141 10 ай бұрын

its possible to use powerpoint to replicate his animations

@iannoezaratechavez4561 7 ай бұрын

I got to a different equation for the answer: Instead of rationalising the fractions I left them as X/√3 and 3X/√3. Then the base of the triangle is 1=4X/√3 + 6X Then you can isolate the X to get the final answer: X=1/(4/√3 + 6) Which is a different equation, but still gets you that same 0.1203...

@zanyboy8k 11 ай бұрын

cant belive i saw this the minute it was uploaded lol. keep making content love the math problems! cheers!!

@Alians0108 11 ай бұрын

He's going to quit because of this comment

@atul5768 11 ай бұрын

ok your not funny

@tplayz3454 10 ай бұрын

Love ur contet plz bring amc or any other Olympiad previous year questions

@mekaindo 6 ай бұрын

He was really excited for discovering something. 😅

@Vengemann 11 ай бұрын

These questions are very fun to solve ngl

@sweetmercury 11 ай бұрын

What software are you using on screen when you make the vids?

@victorldunn9638 11 ай бұрын

... I too would like to know what software is being used please.

@DandoPorsaco-ho1zs 11 ай бұрын

PowerPoint can do this easily.

@sweetmercury 11 ай бұрын

@@DandoPorsaco-ho1zs i see. It looked like something he was working with “live” rather than a preset presentation.

@Playerone1287 10 ай бұрын

112k subs I knew you will grow rapidly Even you knew that because your videos are very simple and quick Last time I saw you had 37k subs some 15 days ago

@DandoPorsaco-ho1zs 11 ай бұрын

I started with the same triangle on the left (sqrt(3)), but I managed to make it slightly more complicated afterwards. In the end, I got the exact same answer, with the same rationalisation, though.

@carmicha 11 ай бұрын

I’d like to know more about how you’re approaching this channel, your content production tools and process, and how it fits into the whole AndyMath empire. But I get that it’s none of my business.

@karlkarlson3502 11 ай бұрын

*DO YOU MOONLIGHT FOR THE CIA? BECAUSE YOU'RE VERY NOSY!*

@p3rryw 11 ай бұрын

Could possibly save a step by noticing the two triangles and similar, so the sides are in a ratio of 1:3… then rather than all the adding up you would know that the total unknown length is 4/route3

@namanhnguyen7933 11 ай бұрын

plus 6x too because it also contains the length of 3 squares, 6x + 4x/root3 = 1

@the_verTigO 8 ай бұрын

For the left triangles i divide x by tan(60) (which is sqrt3) so that's x/sqrt3. For the right triangle I divide 3x by sqrt3 so that's 3x/sqrt3. Everything inbetween is x+2x+3x=6x. x/sqrt3+3x/sqrt3=4x/sqrt3 (4/sqrt3)x+6x=1 x(4/sqrt3+6)=1 x=1/(4/sqrt3+6)

@tomdekler9280 10 ай бұрын

I wonder if this picture would work with any other quadratically growing number of boxes, or would the edges of some boxes be sticking out of the triangle?

@squishygrapeschannel3276 11 ай бұрын

He looks like he actually had fun doing math.

@thedivstuplay3476 11 ай бұрын

Ngl these remind me of i solved olympiads, pretty fun

@Napsteri 7 ай бұрын

What is the program used on videos?

@altogeorge2406 6 ай бұрын

Did you find out?

@Napsteri 6 ай бұрын

@@altogeorge2406 sadly, no.

@KingdomOfDaylightsDauphin 11 ай бұрын

I love these!

@mayislive46 11 ай бұрын

How exciting 🔥🔥🔥

@rishabhmittal9552 11 ай бұрын

3:35 you can just use the difference of two squares

@zOni413 11 ай бұрын

Слишком лёгкая задача. Вспоминаем определение тангенса угла, вспоминаем чему равен тангенс 60° - всё, считай готово. Осталась только чистая арифметика. (Ну а про сумму углов треугольника и про равенство сторон квадрата мне даже и говорить неловко...)

@Datnguyenburh 2 ай бұрын

if we cant use our calculator, it's much harder, but i think we can still use it, and for me, we can use a bit of our knowledge and our calculator is enough, just simplify our calculation and it seems a little easier: 6x(tan60)+4x= tan60 => x(6tan60 + 4) = tan60 => x= (6tan60 + 4) / tan60 and still the same result

@HereForTheComments 11 ай бұрын

Does Andy still check his Patreon? I am hopelessly fascinated with how he does this stuff and I have to know what goes on in his head.

@paulshelley7664 11 ай бұрын

You're very good. Good explanation. Thanks

@nk_w84 11 ай бұрын

Hello there! Thank you for such an amazing video. Even with my poor english language knowledges i understood everything. Nice problem, nice solution. Thx for your work

@Kuwustilam 11 ай бұрын

How exciting!

@tplayz3454 10 ай бұрын

As i did just used tan 60 i e rt 3 to find that small length and got ans very easy

@rayyanmohd2382 10 ай бұрын

cool way simplifying of trigonometry.

@TheTallRaver 11 ай бұрын

Cool!👍👍

@Mike817 11 ай бұрын

When you discovered how to zoom in, you missed the perfect opportunity to say, "How exciting!"™😀

@galatynix 10 ай бұрын

if it wasn't for the 0 and 1, the solution would be a perfect 0.1234567

@sheelakumbhar6411 9 ай бұрын

How exiting!

@OPMfan_00976 11 ай бұрын

Good question. Thank you buddy your content is amazing

@nabil4389 11 ай бұрын

where have you been?

@GregoryFord98 10 ай бұрын

How exciting

@StudyClass10th0 11 ай бұрын

Nice 😮

@irvindalacourt7178 4 ай бұрын

brilliant

@mikep3813 10 ай бұрын

You could have done 20 things wrong in that video, and i would have had no idea.

@tsirahxuan_R 11 ай бұрын

#TIL Square root of number can also be called as radical number..

@Cr1ehcj5g85n 11 ай бұрын

Good content

@cyanophage4351 7 ай бұрын

How radical

@hazxries6228 7 ай бұрын

I feel like there are much easier and faster ways for this

@zunkman1 11 ай бұрын

I would have gone for the obvious that "??" would be 3 times "?" since they are similar triangles. "?" has the height as 1 and "??" has the height as 3. So ?? would be 3?.

@Idran 9 ай бұрын

That's basically already what you do whenever you use one of the standard triangles, honestly.

@bryanscott8675 11 ай бұрын

❤

@Noor-sl5ep 11 ай бұрын

Yeah, i don't know what is going on.

@LM-he7eb 10 ай бұрын

If that is true, then x = 0.1146

@adamconnor1898 6 ай бұрын

Downrated because I dislike problems where you have to remember factoids to solve them. It would be better to derive what the relationships between the legs of the triangle are.