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The pedal curve of an astroid x = acos^3t (1) y = asin^3t (2) with pedal point at the center is the quadrifolium x_p = acostsin^2t (3) y_p = acos^2tsint. (4)

The radial curve of the astroid x = acos^3t (1) y = asin^3t (2) is the quadrifolium x_r = x_0+12acostsin^2t (3) y_r = y_0+12acos^2tsint. (4)

A pair of numbers m and n such that sigma(m)=sigma(n)=m+n-1, where sigma(m) is the divisor function. Beck and Najar (1977) found 11 augmented amicable pairs.

The augmented hexagonal prism is Johnson solid J_(54), which is formed from augmentation of one of the lateral faces of an equilateral hexagonal prism by an equilateral ...

The augmented pentagonal prism is Johnson solid J_(52), which is formed from augmentation of one of the lateral faces of an equilateral pentagonal prism by an equilateral ...

The augmented triangular prism is Johnson solid J_(49), which is formed from augmentation of one of the lateral faces of an equilateral triangular prism by an equilateral ...

The augmented tridiminished icosahedron is Johnson solid J_(64), which is formed from augmentation of the triangular face adjecent to all three hexagons of the tridiminished ...

The augmented truncated tetrahedron is Johnson solid J_(66) constructed by affixing a square cupola to one of the octagonal faces of a truncated cube such that the cupola's ...

The augmented truncated dodecahedron is Johnson solid J_(68) constructed by affixing a pentagonal cupola to one of the decagonal faces of a truncated dodecahedron such that ...

The augmented truncated tetrahedron is Johnson solid J_(65) constructed by affixing a triangular cupola to one of the hexagonal faces of a truncated tetrahedron such that the ...