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Science journals of interest: Scientific American - Nature - New Scientist - Science AAAS - Science Daily

LAST EDITED: March 17, 2015

Here are some interesting links I had stickied:
Yeano's thread: Proving Something is Independent of our Axioms.
Yeano's thread: Algebraic Topology and Model Theory

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Circles inside triangles
Posted: Posted June 12th, 2017 by The Fly

Take any triangle whose sides have length \(a, b, c\). Find the largest area of a circle that fits inside the triangle. Write down a formula for this area in terms of \(a, b, c\). Can you find its radius?

May the Circles and Triangles be with you.

Your best friend,
The Fly


There are 3 Replies

Fly around the circle!

Posted June 12th, 2017 by weid man
weid man

In the case of an isosceles triangle of sides \(a, a, b\), it only takes an easy calculation to show that the largest embedded circular area is given by

\(\Large{ A = \frac14 \pi b^2 \left(\frac{2a-b}{2a+b}\right) }\).

Does that seem right to you?

Edited June 18th, 2017 by The Fly
The Fly

In general, could any triangle be mapped to an isosceles triangle by means of a Möbius transformation?

Edited June 18th, 2017 by The Fly
The Fly
Reply to: Circles inside triangles

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