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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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interview question
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
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
High School
By
shitikanth
on June 21, 2012 | Updated Dec. 6, 2017
A well known triangle
Let \(ABC\) be an acute-angled triangle. Find points \(X, Y, Z\) on sides \(BC, CA\) and \(AB\) such that the perimeter of the triangle \(XYZ\) is minimized.
Mathematics
Geometry
optimization
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