Ultromotion
Studio
Workspace
  • Projects
  • Artifacts
  • AI Builder
  • Browse
Platform
  • Pricing
  • Usage
  • MCP

Browser storage

This device only

Sign in to protect your work and continue on any device.

TermsPrivacyRefunds
Ultromotion
Studio
Browse

Community

Browse projects

Explore animations and lessons from Ultromotion Studio and the community. Preview a project, then make an editable copy.

124 lessons · Official examples are authored by Ultromotion Studio.

Empty scene
1080 × 1080
Hover to play

Area of a Circle: πr²

Watch what happens when we slice a circle into wedges and rearrange them. The pieces form a rectangle-like shape with width πr and height r—revealing exactly where A = πr² comes from.

Why Is the Area of a Circle πr²?·Math·0:30 · 1 scene
Hover to play

One Twist Erases the Other Side

This ribbon looks two-sided. Can one half-twist turn it into a surface with just one side? A local patch can look ordinary while the whole surface behaves differently. A Möbius strip has one continuous side and one boundary.

Ultromotion StudioOfficial example·3D & visual mathematicsPro·0:48 · 1 scene
Hover to play

Six Pyramids Fit Inside One Cube

Cut a cube from its center to all six faces. How can six pyramids fill it without leaving a gap? The six pyramid volumes add to the cube volume. This decomposition makes the pyramid volume formula visible in a symmetric case.

Ultromotion StudioOfficial example·3D & visual mathematicsPro·0:54 · 1 scene
Hover to play

A Hole Changes the Counting Rule

Count vertices, edges and faces on a closed solid. Why does adding one hole change the answer? Euler characteristic records topology, not the particular triangulation. For a closed orientable surface, each extra handle lowers it by two.

Ultromotion StudioOfficial example·3D & visual mathematicsPro·0:51 · 1 scene
Hover to play

A New Solid Hides at Every Face Center

Mark the center of each cube face. What new solid appears when neighboring face centers are connected? Duality exchanges vertices with faces while preserving the edge relationships. The cube and octahedron are a dual pair.

Ultromotion StudioOfficial example·3D & visual mathematicsPro·0:48 · 1 scene
Hover to play

A Circle Climbs Into the Third Dimension

A point keeps circling, but it rises at the same time. Why does its path become a helix? A helix combines circular motion with steady translation along an axis. The same geometry appears in threads and coiled forms.

Ultromotion StudioOfficial example·3D & visual mathematicsPro·0:55 · 1 scene
Hover to play

A Circle That Climbs Becomes a Helix

What happens when a circle keeps turning while its height keeps increasing? A helix combines periodic motion in two coordinates with steady progress in the third.

Ultromotion StudioOfficial example·3D & visual mathematicsPro·0:45 · 1 scene
Hover to play

One Rotating Radius Draws Five Petals

This flower uses no hand-drawn petals. What rule is drawing it? Five petals emerge from one polar equation. The shape follows the rule, rather than a list of drawn pieces.

Ultromotion StudioOfficial example·3D & visual mathematics·0:48 · 1 scene
Hover to play

This Surface Bends Up and Down at Once

Can a surface curve upward and downward at the very same point? A zero slope does not guarantee a minimum. In several dimensions, inspect more than one direction.

Ultromotion StudioOfficial example·3D & visual mathematicsPro·0:43 · 1 scene
Hover to play

A Wheel's Edge Does Not Travel in a Circle

A dot sits on the edge of a rolling wheel. What path does it leave behind? The motion you see depends on the reference frame. A circle around a moving center becomes a cycloid on the ground.

Ultromotion StudioOfficial example·3D & visual mathematics·0:51 · 1 scene
Hover to play

Why a Twenty Percent Drop Needs a Bigger Recovery

A price drops twenty percent. Why does a twenty-percent rise fail to restore it? Opposite percentages use different bases. Equal percentage changes do not generally cancel.

Ultromotion StudioOfficial example·Math & reasoning·0:38 · 1 scene
Hover to play

Why One Expiring Item Can Cause a Traffic Spike

One cache entry expires. Suddenly the origin receives a burst of identical work. Where did it come from? High hit rates do not prevent expiry spikes. Design what happens when a popular value disappears.

Ultromotion StudioOfficial example·System design·0:42 · 1 scene