Five points are located in an equilateral triangle with 10-inch sides (or on its perimeter).
What’s the maximum distance between the two closest points?
(In reply to
re(2): A guess - A proof by Ady TZIDON)
Since BS and SH has together furnished a well explained solution, all that remains for me is to comment on the title.
This problem employs "pigeonhole principle" to achieve the solution.
It goes without saying that Johann Peter Gustav Lejeune Dirichlet (1805-1859) was a famous German mathematician.
WIKIPEDIA says:
"Although the pigeonhole principle appears as early as 1624 in a book attributed to Jean Leurechon, it is commonly called "Dirichlet's box principle" or "Dirichlet's drawer principle" after an 1834 treatment of the principle by (Johann) Peter Gustav Lejeune Dirichlet under the name Schubfachprinzip ("drawer principle" or "shelf principle")"
Since the instrument (pigeonhole principle) employed in solving the problem is named after Prof. Dirichlet, the meaning and significance of the title is self evident.
Edited on June 14, 2022, 3:54 am
re(3): A guess - A proof
