# Solution: Hidden Reuleaux Triangle

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**Published on Aug 23, 2018**- We discover a connection between obtuse angles and the Reuleaux triangle while solving a geometric probability problem.

Congratulations to Kevin M, Benjamin Wang, Zain Majumder, attyfarbuckle, Throxs, Beshoy Nabil, Richard Chen, NoName, Allan Lago, and dominofan238 for successfully solving the last week's math challenge question! Kevin M was the first person to solve the question.

Your support is truly a huge encouragement.

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qqqquito9 months ago^{+2}In a museum in China, I saw a number of Reuleaux tetrahedrons, the 3D version of Reuleaux triangles, of the same size placed on the flat floor of a limited area, and a cart with a flat bottom are placed on top of these Reuleaux tetrahedrons. A visitor can sit in the cart while the cart is being pushed by someone else. As you presume, the cart moves as if on a flat surface while those tetrahedrons beneath roll in sort of a nondescript manner.

LetsSolveMathProblems9 months ago^{+1}Wow, that sounds interesting! I probably wouldn't want to have a car with Reuleaux tetrahedrons as wheels, though. =)

Martin Howler9 months agoCan you do a proof of Louisville’s Theorem? Thanks!

Terek9 months ago^{+1}Could you help to find solution to this limit please: limx->0 (sin(tan(x))+tan(sin(x)))/(arcsin(arctan(x))-arctan(arcsin(x)))

OR

sin(tan(x))-tan(sin(x))

lim x->0--------------------------------------------------------------

arcsin(arctan(x))-arctan(arcsin(x))

Patrick9 months agoThanks for the video

SherTheDugtrio_YT9 months agoLet's Make Math Problems and Solve It!

Adlet Irlanuly9 months ago^{+2}I like how you end up your videos with a high calm voice in a joyful tone and then goes pause.

Your videos have become for me as some kind of favourite show such as SNL.

Thanks for all of your work

As always , this video is awesome.

LetsSolveMathProblems9 months agoI appreciate your compliment, Adlet Irlaunly! Commenters like you make my day. =)

101001010010010109 months ago^{+1}I think it's supposed to be pi over 3 for 60 degrees

JHawk245 months ago^{+1}he's not talking about radians to degrees, he was doing the ratio of the angles to the whole circle times the area, so 60 / 360 * π which is π/6

Typo9 months ago^{+1}the x in Reuleaux is silent

madhav 's talks9 months agoWhere is challenge of today??

mark crawford9 months ago^{+1}An interesting fact about Reuleaux triangles... They have constant diameter. Similar to a circle, they longest line segments inside the shape all have the same length.

mark crawford9 months ago^{+2}@San Seng Yes, but not in the "usual" sense. It makes for a bumpy ride if placed on an axle. However if two Reuleaux triangles with the same diameter are sandwiched between parallel surfaces, they can roll between the surfaces and the distance between the surfaces won't change.

San Seng9 months agoMeaning it can roll somewhat like a wheel, correct?

jonathan nicholson9 months ago^{+1}it looked like the Inscribed Angle theorem, but I forgot the theorem

Seth Harwood9 months ago^{+9}It's called the Theorem of Thales

Varad Mahashabde9 months ago^{+1}Our teacher simply called it angle in a semicircle

MrPanzerTanzer9 months agoOr the Thales Circle

Felipe Lorenzzon9 months ago^{+12}I suggest you could use some website that allows viewers to write with Latex. It would be much easier to express the solution.