# Thread: Math Puzzle in The NYTimes....

1.  Math Puzzle in The NYTimes.... In today's Science section....

How many triangles are formed by six intersecting lines? Given that no two lines are parallel, and there are no points where more than two lines intersect.  2. Originally Posted by Conor Dary In today's Science section....
How many triangles are formed by six intersecting lines? Given that no two lines are parallel, and there are no points where more than two lines intersect.
I'm still trying to figure how many angels can dance on the head of a pin . . .  3. Originally Posted by Conor Dary In today's Science section....

How many triangles are formed by six intersecting lines? Given that no two lines are parallel, and there are no points where more than two lines intersect.
For each of the six lines, every one of the five (non-parallel) lines crosses exactly once. For each of those pair of lines each of the four remaining lines must cross to form a triangle. That defines 6×5×4=120 line combinations that form triangles, but does not take into account that abc, bac, cba, etc are the same triangle. There are 3×2×1=6 such ways to describe each triangle, so there are 120/6=20 unique triangles. There is a fancy mathematical way to write this, but I forget how.  4. Originally Posted by Atticus I'm still trying to figure how many angels can dance on the head of a pin . . .
it's actually the point of a pin and the answer is 8.6766×10exp49

https://improbable.com/airchives/pap...angels-7-3.htm  5. Originally Posted by gh it's actually the point of a pin and the answer is 8.6766×10exp49
https://improbable.com/airchives/pap...angels-7-3.htm
From the article:

"How many angels can dance on the head of a pin?" has been a major theological question since the Middle Ages.
but I see that this argument is for the point. I like the eloquence of the math!  6. 20 is the answer....  7. Originally Posted by Atticus I'm still trying to figure how many angels can dance on the head of a pin . . .
Im trying to figure out how many angles can fit on the head of a pin.  8. It depends on the angles between the angels.  • You may not post new threads
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