Follow your curiosity

What discovery has been shared with you?

FACTREE gives you something interesting to discover every day — and something worth talking about together.

Start with one fact. Explore it, go deeper, then follow whichever branch catches your imagination.

Choose subjects for a surprise

Exploring any topic

Begin your discovery

Your next discovery is one click away.

Choose one or more subjects above, or leave Any Topic selected and let curiosity decide.

Mathematics

Conic Sections in Coordinate Geometry

Quick fact

Remarkably, one family of curves—ellipses, parabolas, and hyperbolas—emerges from slicing a double cone at different angles: a shallow tilt gives a circle or ellipse, a parallel slice gives a parabola, and a steep slice gives a hyperbola. This single geometric operation unites orbits, satellite dishes, and even the paths of comets.

Why this is interesting

You've probably seen a parabola when you toss a ball, and an ellipse in the orbit of a planet—but did you know these shapes are all made by slicing a cone with a single flat plane?