Fox 197

Those apes keep juglin'

http://www.8foxes.com/

Fox 198

http://www.8foxes.com/

This is the beginning of a class of foxes with random processes.

The above process is a special form of a random walk on the plane.
We believe that this process is new! If you see something similar in literature, please let us know.

"Uniformly selected" means that every direction has an equal chance of being selected.
In other words: direction ~ Uniform[0, 360].
Point O is the origin. Generation of point A is irrelevant since OA does not change whether there will be a triangle or not at the end of the process.
Also, it is not important but assume that the random directions are generated clock wise.
The answer has not been confirmed yet, let us know if you find something very different.

Fox 196

The problem has been modified for the answer was not precise.

Let us know if you see a problem.

http://www.8foxes.com/

Fox 195

http://www.8foxes.com/

Fox 60

http://www.8foxes.com/

Fox 194

http://www.8foxes.com/

Fox 193

Inspired from a question submitted by Ajit.

Fox 192

http://www.8foxes.com/

Fox 191

http://www.8foxes.com/

Fox 190

http://www.8foxes.com/

Fox 189

Fox 7

Fox 188

Fox 187

Fox 13

Options were updated to make it more challenging.

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 141

Look carefully!
You'll find the same seal
on the earth and in the heavens!
--- Dervish Fox

Fox 155

Fox 183

Fox 185

Red Fox: Hey Polar, check this out; a unique configuration of a circle and a square! Ain't it beautiful?
Polar Fox: Not bad! What'd you have to say about it?
Red Fox: Here I say all fractions are reachable by adding simple tangents and other similar connections.
Polar Fox: Hmmm! Is that not a too strong statement?
Red Fox: Well, imagine drawing new tangents and line segments between existing intersection points.
If you keep on doing that, soon those intersection points will numerically-explode. And you can compute any fraction similar to the answer.
Polar Fox: OK. There are infinitely-many integers but NONE satisfies: a-cube plus b-cube equals to c-cube. Do you have one such a, b, c?
Red Fox: I know Fermat says NO. And I see your point. But this is not the same thing. You can probably span the whole plane like this.
Polar Fox: Fine, give me an 11/19 then.
Red Fox: I got to work on that.

Fox 184

Fox 182

Does the above have any "haiku" value?
Probably not much :)

Fox 181

Fox 180

Fox 59

Fox 179

Fox 177

Even though material interests may drive the human behavior,

there are still worldly images and unworldly lyrics inspring novelty,

reminding them to do good.

How can you draw righteousness on a board?

Does it really matter if charity is concave or convex?

--- Fox Weber

Fox 178

Polar Fox: Dude, did you get any permission to use a trademark?
Red Fox: What permission? This is a public service we are engaged in.
Polar Fox: Oh really? Still I say that logo has an owner. It says in its corner, see.
Red Fox: Go ahead; let those capitalist scumbags know about it.
Polar Fox: Oh come on Red, stop acting like a mild Chávesian socialist. You spent all your time in youtube and facebook.
Red Fox: Yeah, I am extending my base in the internet for a revolution.
Polar Fox: Yeah, sure. The only thing I see revolving is your chubby belly.

Fox 175

http://www.8foxes.com/Home/175
See how it gets harder :)

Fox 174

www.8foxes.com/Home/174

Fox 176

General case reveals the answer.
This is not terribly hard!
http://www.8foxes.com/Home/176

Fox 173

One step into difficuilty...