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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
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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
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 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
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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