If three points lie on the graph of y=1/x, so will their orthocenter.

The plane separating the near and far sides of the sun rolls on a circular cylinder.

Happy pi day

Somehow non-obvious to me: The six points, consisting of two arbitrary points and their tangency points to a given conic, will always lie on a conic.

A picture of a sphere with two great circles exhibits 6 points sharing a conic.

No matter how you view the bicylinder solid, the 8 corners on the outline always lie on some conic.

From the intersection of two circles, the angle bisector of the radii meets both common tangents at a point.

For any triangle, the feet of the secondary altitudes lie on a circle.

Carnot's Theorem is a generalization of the Pythagorean Theorem. The total red area equals to the total blue area.

Our #SIGGRAPH 2022 paper: Covector Fluids. With a simple modification of the advection step, a fluid solver respects the Kelvin circulation law and displays richer vortical structures. youtu.be/jM1FNiVYofI

For each corner of any triangle, pick an arbitrary angle and draw two rays, each apart from the adjacent edges by that angle. Then we will get a hexagon whose opposite diagonals are concurrent.

The chords of intersections from 3 (commonly oriented) parabolas always meet at a point.

Consider a vertical and a horizontal parabolas sharing the same vertex. The tangents at their intersection will meet the contact points of their common tangent!

For any two parabolas, the foci and all intersections of the common tangents always lie on a circle.

Do you know how to come up with this vector identity about cofactor matrix and cross product? (Check out our course on #ExteriorCalculusInGraphics)

If a matrix field has curl-free rows, then its cofactor matrix has div-free rows. #ExteriorCalculusInGraphics

For any given quadrilateral, the lines that connect the midpoints of its sides and diagonals intersect at a single point.

This is neat. The gradient of the log of determinant is inverse transpose.

There are only at most 26^60 integers that can be defined in under sixty letters. Therefore there must exist "the smallest positive integer not definable in under sixty letters" (which is a phrase with 57 letters).

Checkout our new paper #SIGGRAPH2023 involving interesting study on fluid dynamics and algebraic topology.