MHB What is the Probability of Distances in an Equilateral Triangle?

Click For Summary
The discussion focuses on determining the probability that a randomly chosen point P within an equilateral triangle T has a corresponding point Q within T that is more than the altitude of T away from P. The altitude of an equilateral triangle can be calculated using its side length. The suggested solution involves geometric probability and the properties of distances within the triangle. Participants explore the implications of the triangle's symmetry and uniform distribution in calculating the desired probability. The conversation emphasizes the mathematical principles involved in solving this geometric probability problem.
lfdahl
Gold Member
MHB
Messages
747
Reaction score
0
A point $P$ is chosen at random with respect to the uniform distribution in an
equilateral triangle $T$. What is the probability that there is a point $Q$ in $T$ whose distance
from $P$ is larger than the altitude of $T$?
 
Mathematics news on Phys.org

Attachments

  • Triangle probability calculation.PNG
    Triangle probability calculation.PNG
    42.5 KB · Views: 118

Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
View full post »

Similar threads

Undergrad Prove that a triangle with lattice points cannot be equilateral
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad What is the name of the triangle centre point with 120° subtended vertices?
  • · Replies 2 ·
Replies
2
Views
1K
MHB Prove Area of Equilateral Triangle
  • · Replies 9 ·
Replies
9
Views
2K
MHB Show that there are points Q,R on C such that the triangle PQR is equilateral.
  • · Replies 1 ·
Replies
1
Views
1K
MHB Distance between points in a triangle
  • · Replies 1 ·
Replies
1
Views
3K
MHB Please find the side length of an equilateral triangle
  • · Replies 3 ·
Replies
3
Views
2K
MHB What's the Probability That Area of MNP is ≥ Half of ABC?
  • · Replies 6 ·
Replies
6
Views
3K
MHB Proof Quest: Non-Equilateral Triangle Enclosing Point Z
  • · Replies 3 ·
Replies
3
Views
2K
MHB Find the area of an equilateral triangle
  • · Replies 6 ·
Replies
6
Views
2K
MHB [ASK] Find the volume of Pyramid in a Cube
  • · Replies 6 ·
Replies
6
Views
3K