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In any tree, the number of dissimilar points minus the number of dissimilar lines plus the number of symmetry lines equals 1.

An egg-shaped curve. Lockwood (1967) calls the negative pedal curve of an ellipse with eccentricity e<=1/2 an ovoid.

The two-dimensional version of the ham sandwich theorem.

A papal cross is a cross having three crossbars. A schematic polyomino version of a papal cross is illustrated above.

An m×n matrix which gives the possible outcome of a two-person zero-sum game when player A has m possible moves and player B n moves. The analysis of the matrix in order to ...

A curve given by the Cartesian equation b^2y^2=x^3(a-x). (1) It has area A=(a^3pi)/(8b). (2) The curvature is kappa(x)=(2b^2(3a^2-12ax+8x^2))/(sqrt(x)[4b^2(a-x)+(3a-4x)^2x]). ...

For some range of r, the Mandelbrot set lemniscate L_3 in the iteration towards the Mandelbrot set is a pear-shaped curve. In Cartesian coordinates with a constant r, the ...

A pentagon is a five-sided polygon. Several special types of pentagons are illustrated above. In particular, a pentagon with vertices equally spaced around a circle and with ...

A singular point such that every neighborhood of the point intersects itself. Pinch points are also called Whitney singularities or branch points.

If a circular pizza is divided into 8, 12, 16, ... slices by making cuts at equal angles from an arbitrary point, then the sums of the areas of alternate slices are equal. ...