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It is conjectured that every tree with e edges whose nodes are all trivalent or monovalent can be given a "magic" labeling such that the integers 1, 2, ..., e can be assigned ...

Every point which can be constructed with a straightedge and compass, and no other points, can be constructed using identical matchsticks (i.e., identical movable line ...

The dual of the snub dodecadodecahedron U_(40) and Wenninger dual W_(111).

Let R be a plane region bounded above by a continuous curve y=f(x), below by the x-axis, and on the left and right by x=a and x=b, then the volume of the solid of revolution ...

The unique 1-polyomino, consisting of a single square.

The negative real axis is the portion of the real axis with x<0.

A polygonal number of the form O_n=n(3n-2). The first few are 1, 8, 21, 40, 65, 96, 133, 176, ... (OEIS A000567). The generating function for the octagonal numbers is ...

The illusion illustrated above in which the bounding rectangle and inner square both appear distorted.

Given a regular pentagon of unit area, mean triangle area of a triangle picked at random inside it is given by the n=5 case of polygon triangle picking, A^_ = ...

The pentagonal cupola is Johnson solid J_5. Its faces consist of 5 equilateral triangles, 5 squares, 1 pentagon, and one decagon. The surface area and volume of the ...