Search Results for ""

If two intersections of each pair of three conics S_1, S_2, and S_3 lie on a conic S_0, then the lines joining the other two intersections of each pair are concurrent (Evelyn ...

The converse of Pascal's theorem, which states that if the three pairs of opposite sides of (an irregular) hexagon meet at three collinear points, then the six vertices lie ...

If three conics pass through two given points Q and Q^', then the lines joining the other two intersections of each pair of conics P_(ij)P_(ij)^' are concurrent at a point X ...

A triangle and its polar triangle with respect to a conic are perspective.

If two points A and A^' are inverse with respect to a circle (the inversion circle), then the straight line through A^' which is perpendicular to the line of the points AA^' ...

Let H be a heptagon with seven vertices given in cyclic order inscribed in a conic. Then the Pascal lines of the seven hexagons obtained by omitting each vertex of H in turn ...

Consider the decimal expansion of the reciprocal of the number seven, 1/7=0.142857142857...=0.142857^_, (1) which is a repeating decimal. Now take overlapping pairs of these ...

A curve and its polar reciprocal with regard to the fixed conic have the same Halphen transformation.

A triangle that is equal to its polar triangle with respect to a given conic is said to be self-polar with respect to that conic. Any triangle is self-polar with respect to ...

If S_1, S_2, and S_3 are three conics having the property that there is a point X, not on any of the conics, lying on a common chord of each pair of the three conics (with ...