Symmetry

Plot the graph of x^y = y^x in the first quadrant and explain its properties.

An equilateral triangle is sitting on top of a square. What is the radius of the circle that circumscribes this shape?

What groups of transformations map a regular pentagon to itself?

Each of these solids is made up with 3 squares and a triangle around each vertex. Each has a total of 18 square faces and 8 faces that are equilateral triangles. How many faces, edges and vertices does each solid have?

Weekly Problem 28 - 2013
Two lines meet at a point. Another line through this point is reflected in both of these lines. What is the angle between the image lines?

Place the numbers 1, 2, 3,..., 9 one on each square of a 3 by 3 grid so that all the rows and columns add up to a prime number. How many different solutions can you find?

When dice land edge-up, we usually roll again. But what if we didn't...?

Points off a rolling wheel make traces. What makes those traces have symmetry?

Can you devise a fair scoring system when dice land edge-up or corner-up?

Can you show that you can share a square pizza equally between two people by cutting it four times using vertical, horizontal and diagonal cuts through any point inside the square?