# Math Puzzle in The NYTimes....

• 08-27-2019, 09:46 PM
Conor Dary
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.
• 08-27-2019, 10:57 PM
Atticus
Quote:

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 . . .
• 08-28-2019, 03:13 PM
Master403
Quote:

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.
• 08-28-2019, 03:47 PM
gh
Quote:

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
• 08-28-2019, 04:31 PM
Atticus
Quote:

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:

Quote:

"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!
• 08-29-2019, 03:55 PM
Conor Dary