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High School
By
True IMO
on July 21, 2016 | Updated Jan. 4, 2018
International Mathematical Olympiad 2016 Problem 3
Let \(P = A_1, A_2 \dots A_k\) be a convex polygon on the plane. The vertices \(P = A_1, A_2 \dots A_k\) have integral coordinates and lie on a circle. Let \(S\) be the area of \(P\). An odd positive …
Mathematics
Geometry
imo
imo 2016
polygon
0
High School
By
Shiva Kintali
on June 6, 2014 | Updated Jan. 4, 2018
Constructible polygons
A constructible polygon is a regular polygon that can be constructed with compass and straightedge. For example, a regular pentagon is constructible with compass and straightedge while a regular hepta…
Mathematics
Geometry
polygon
0
High School
By
Shiva Kintali
on June 28, 2012 | Updated Dec. 6, 2017
Integral Rectangles
A large rectangle is partitioned into smaller rectangles, each of which has either integer height or integer width or both. Prove that the large rectangle also has this property.
Mathematics
Puzzles
Geometry
Puzzles
interview question
math puzzle
0
Undergraduate
By
Shiva Kintali
on June 10, 2012 | Updated Dec. 6, 2017
Stick triangle
A stick is broken at random into three pieces. What is the probability that the pieces can form a triangle?
Mathematics
Puzzles
Geometry
Probability
Puzzles
math puzzle
0
High School
By
Shiva Kintali
on May 7, 2014 | Updated Jan. 4, 2018
Quarter past three
How many degrees are there in the angle between the hour and minute of a clock when the time is a quarter past three ?
Mathematics
Puzzles
Geometry
Puzzles
geometry puzzle
0
Undergraduate
By
Shiva Kintali
on June 6, 2012 | Updated Dec. 6, 2017
Happy Ending Problem
Prove the following : Any set of five points in the plane in general position has a subset of four points that from the vertices of a convex quadrilateral. For any positive integer \(N\), any suffic…
Mathematics
Combinatorics
Geometry
counting
0
Undergraduate
By
Shiva Kintali
on June 17, 2012 | Updated Dec. 6, 2017
Turan geometry
Let \(x_1, x_2, \dots, x_n\) be a set of diameter one in the plane. Prove that the maximum number of pairs of points at distance greater than \(1/\sqrt{2}\) is \(\lfloor n^2/3\rfloor\).
Mathematics
Geometry
Graph Theory
extremal graph theory
0
Undergraduate
By
Shiva Kintali
on Sept. 28, 2013 | Updated Jan. 4, 2018
Ramsey points
Let \(P\) be a set of \(n\) points in the plane, such that each 4-tuple forms a convex 4-gon. Then \(P\) forms a convex n-gon. Let \(P\) be a set of five points in the plane, with no three points c…
Mathematics
Geometry
geometry puzzle
ramsey theory
0
High School
By
Shiva Kintali
on June 16, 2013 | Updated Jan. 4, 2018
Pick's theorem
Let \(P\) be a polygon constructed on a grid of equal-distanced points (i.e., points with integer coordinates) such that all the polygon's vertices are grid points. Let \(I\) be the number of lattice …
Mathematics
Geometry
polygon
0
Undergraduate
By
Shiva Kintali
on June 6, 2012 | Updated Dec. 6, 2017
Distances between points in a plane
Let \(S\) be a set of \(n \geq 3\) points in the plane such that the distance between any two points is at least 1. Prove that there are at most \(3n - 6\) pairs of points at distance exactly 1. Pro…
Mathematics
Combinatorics
Geometry
counting
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