Night 1 - Townies please check threads for a surprise... ends in 48 hours.

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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The Euler Line
Posted: Posted September 10th, 2017 by The Fly

Take any triangle (as shown here). It has 3 kinds of "centers":

1. You can look at its usual center of mass. (Where it balances out.)

2. You can look at its orthocenter -- that is, the point where the perpendicular altitutes all cross. (And all 3 altitudes do cross at the same point.)

3. You can look at the center of the circle that goes thru its corners. (There's only one such circle.)

It turns out that all these three points are on the same line (i.e., they're colinear). That line is called the Euler line of the triangle. (The one exception is when all these points are the same point when the triangle is an equilateral.) I don't think this is hard to work out and show, but this result is interesting to know.

Have fun,
The Fly


There are 1 Replies

PS-I wished there was a way to control the size of the linked pic, but didn't know how to. Sorry it came out too big.

Posted September 10th, 2017 by The Fly
The Fly
Reply to: The Euler Line

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