Problem 274: Isosceles Triangle, 80-80-20, Angles
Sunday, May 15, 2011
The 80-80-20 Triangle
Is there anything else that could be said about the 80-80-20 triangle?
Problem 358. Isosceles triangle 80-80-20, Circle, Angles, Congruence.
Problem 274: Isosceles Triangle, 80-80-20, Angles
Problem 274: Isosceles Triangle, 80-80-20, Angles
Monday, May 9, 2011
A collection of Math Olympiad problems
(1) Find the smallest natural number which is a multiple of 2009 and whose sum of
(decimal) digits equals 2009.
(6) Find all primes p such that p^2 – p + 1 is a perfect cube.
(decimal) digits equals 2009.
(2) Find all integer solutions of the equation 3^x - 5^y = z^2
(3) Solve in integers the equation 12^x + y^4 = 2008^z
(4) Determine all pairs of natural numbers (x, n) that satisfy the equation
(5) Determine all pairs (x, y) of integers such that
x^3 + 2x + 1 = 2^n
(5) Determine all pairs (x, y) of integers such that
1 + 2^x + 2^(2x+1) = y^2
(6) Find all primes p such that p^2 – p + 1 is a perfect cube.
(7) Let a, b, c be positive real numbers. Prove the inequality
(a^2 / b) + (b^2 / c) + (c^2 / a) >= a + b + c + 4(a – b)^2 / (a + b + c)
When does equality occur ? Thursday, May 5, 2011
Wednesday, May 4, 2011
A Proposal to End the Practice of Gerrymandering
Using a precise mathematical formula, it is possible to redraw district lines fairly and bring competitiveness back to congressional races
Drawn Together: Can Math Nerds Beat Gerrymandering?
Gerrymandering: Why Your Vote Doesn't Count
Subscribe to:
Posts (Atom)