A Classic Japanese Circle Problem.

Today we want to find out, how the 3 radii of the tangent circles are connected. Not sure if this is a competitive maths problem or not, OP did not specify. But nonetheless I find the result to be highly satisfying :) Enjoy! =)

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[PapaFlammy]

*_Hey bois and grills, thanks for watching <3 Hope you like today's video and if you did, please make sure to check out some of today's relevant links! :3_*
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[gcewing]

This looks very useful. The next time I'm without a calculator and I have a pair of resistors for which I only know the squares of their resistances, and I need to know the conductance of their parallel combination, all I need to do is draw a diagram with three circles!

[Marc]

"I am going to call it r, because I just don't care." mathematicians! D:

[ascaniuspotterhead]

A while ago I tried to solve this problem in my art lessons in school with some friends. We weren’t able to to it. Later I tried it out with analytic geometry and had like the biggest mess on my paper. That the solution is so simple is really cool thx papa flammy

[georgecaplin]

Me: “Gonna learn some maths, LET’S DO THIS!”

FM: “Deez nuuuts!”

[DerSpinneman]

Love how he starts out slow and a little uneasy but once he starts doing math he goes super speed without stopping

[integralboi]

That title is familiar, it’s almost as if some other maths YouTuber made a vid on this problem.

[ALisztf]

4:00 the dude in bottom left scares me, lol, tought it was a real person LMAO

[youngmathematician]

5:40 Is that the Parker circle I see here?

[assassin]

I legit thought this was a Michael Penn video until I heard "A huge thanks to my Patreon supporters for making this episode possible" in that classic Papa Flammy voice.

[sarthaktharaney]

A small nut is not always small, its all a matter of perspective

[sharpman]

This is what I really like in your videos, they are always really 'light' but still interesting.

[AngadSingh-bvvn]

"Lets start with these two big nuts that we have right here, these nuts, just look at these nuts " I dare you to read that in monotone.

[siddharthabhattacharya]

It's simple and straightforward by descartes theorem

[Vijwal]

This question was actually asked in my JEE mains exam to get admission in undergrad Universities. This question can also be done using direct common tangent method.

[reall]

when i first came to your channel, i thought "huh, a crazy german memer teaching maths? sounds like a scam"

very pleased to say that it is in fact a pyramid scheme, and a good one at that. never stop!

[centsant]

I remember this from high school, ah nostalgia

[kiiometric]

I have a question, does that formula also apply for any 3 circumferences? Or do they have to be standing on a straight line?

[kafkayash]

It's intresting ! If you actually make left and right circles as unit circles and middle circles touching the both same way of and continuing the the same pattern from middle circle i.e circle in middle has other circle touching it externally and also thouches the right circle, if you continue this pattern or arrangement for infinitely many circle, and the area of entire setup you get" zeta(4)*pi" aka pi^5/90.

[bjap]

Sees Thumbnail:
A big daddy Circle collides with semi big mommy circle and makes a little baby circle.