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A quartic surface which is the locus of zeros of the determinant of a symmetric 4×4 matrix of linear forms. A general symmetroid has 10 ordinary double points (Jessop 1916, ...

A surface given by the parametric equations x = A(u-a)^m(v-a)^n (1) y = B(u-b)^m(v-b)^n (2) z = C(u-c)^m(v-c)^n. (3)

In general, a tetrahedron is a polyhedron with four sides. If all faces are congruent, the tetrahedron is known as an isosceles tetrahedron. If all faces are congruent to an ...

The term "twisted sphere" is used to mean either a projective plane (Henle 1994, p. 110) or the corkscrew surface obtained by extending a sphere along a diameter and then ...

The vertex triangle of two distinct circumcevian triangles or circumanticevian triangles is perspective to the reference triangle. In addition, the vertex triangles of the ...

A triangle with side lengths a, b, and c and triangle area Delta satisfies a^2+b^2+c^2>=4sqrt(3)Delta. Equality holds iff the triangle is equilateral.

Consider three mutually tangent circles, and draw their inner Soddy circle. Then draw the inner Soddy circles of this circle with each pair of the original three, and ...

The Brocard circle, also known as the seven-point circle, is the circle having the line segment connecting the circumcenter O and symmedian point K of a triangle DeltaABC as ...

The figure determined by four lines, no three of which are concurrent, and their six points of intersection (Johnson 1929, pp. 61-62). Note that this figure is different from ...

All the propositions in projective geometry occur in dual pairs which have the property that, starting from either proposition of a pair, the other can be immediately ...