Fox 324

Before starting to publish received solutions for earlier foxes, let's start with a new one. Here, "random selection" means that points P and Q are uniformly distributed along 2 parallel sides.

Ahh, yes, expected value of the "ratio of" the bigger area to the smaller one is asked - obviously. Let's give some leeway to minor mistakes in our life. "Perfect" may sometimes be boring!

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Fox 307 - Solutions

Two solutions to Fox 307...

by Bleaug:


by Bob Ryden:

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Fox 307

This is related to Proposition 4 in Book of Lemmas by Archimedes.

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Fox 124 - Solution

Bob Ryden provided this solution to Fox 124.

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Fox 242 - Counterexample-2

Yu claims:
A rectangle is a trapezoid. The shaded area (2 equal triangles) = ¼ of the rectangle.


The above trapezoid has the same area as the rectangle above. As P approaches Q, the height of the upper shaded triangle increases faster than the height of the lower shaded triangle decreases. .: the shaded area > ¼ of the trapezoid.

Fox 246

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Fox 242 - Counterexample

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Bleaug has submitted this counterexample. He smells right :)

Easiest way is to get a counter-example:
assume the upper side of the trapezoid collapses to a single point,
the pink area corresponds to 1/4 of the trapezoid/triangle area.
The (non-empty) blue area is in excess.

Fox 230

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Fox 227

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Fox 212

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Fox 211

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Fox 206

We have some work on this, but not the final solution.

Please post your result here if you can find one.

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Fox 203

203 is a simple but really elegant problem from Newzad's blog.

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Fox 199

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Fox 192

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Fox 82

Forget the numbers,

see the essense.

Skip the flesh,

find the soul!

Fox 186

Submitted by: http://geometri-problemleri.blogspot.com

You can find a more generalized version here in Newzad's blog.

Fox 81

Go beyond your numerical mind.
Think simple!

Forget about trigonometry.

Just drawn lines on the sand, like Euclid!

Fox 174

www.8foxes.com/Home/174

Fox 173

One step into difficuilty...