# 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.

• qqqquito 9 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.

• LetsSolveMathProblems  9 months ago +1

Wow, that sounds interesting! I probably wouldn't want to have a car with Reuleaux tetrahedrons as wheels, though. =)

• Martin Howler 9 months ago

Can you do a proof of Louisville’s Theorem? Thanks!

• Terek 9 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))

• Patrick 9 months ago

Thanks for the video

• SherTheDugtrio_YT 9 months ago

Let's Make Math Problems and Solve It!

• Adlet Irlanuly 9 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.

• LetsSolveMathProblems  9 months ago

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

• 10100101001001010 9 months ago +1

I think it's supposed to be pi over 3 for 60 degrees

• JHawk24 5 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

• Typo 9 months ago +1

the x in Reuleaux is silent

• madhav 's talks 9 months ago

Where is challenge of today??

• mark crawford 9 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 crawford 9 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 Seng 9 months ago

Meaning it can roll somewhat like a wheel, correct?

• jonathan nicholson 9 months ago +1

it looked like the Inscribed Angle theorem, but I forgot the theorem

• Seth Harwood 9 months ago +9

It's called the Theorem of Thales

• Felipe Lorenzzon 9 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.