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

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).

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

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

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

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

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

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!

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

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.

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

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

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

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

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

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

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.

Happy pi day

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

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