Math

Pantograph

Draw with two pencils coupled by a brass linkage. Compare the original Q and its enlarged copy P on a wooden drawing board.

By Mykhailo Makarov

Actual application image

What happens

Draw with two pencils coupled by a brass linkage. Compare the original Q and its enlarged copy P on a wooden drawing board. The joints keep P = kQ. Old ink stays on the paper when k changes. Dashed circles bound the reach of Q; input outside that ring is clamped to it.

Try this

Draw on the paper with the left mouse button: Q guides the copy P. Right drag rotates the board; the wheel zooms.

Equations used in the module

Equations
P = kQ

Related experiments

Back to catalogue

Math

Constant width

Turn the parallel calipers around a Reuleaux triangle, circle and ellipse. The first two keep their width; the ellipse does not. The displayed perimeter uses a fine polygonal approximation.

Math

Tangent circles

Fit a fourth disc between three touching discs until it touches all of them, with the narrowest gap magnified; compare its curvature with Descartes' relation, then find the second solution - an enclosing circle, a line or an outside circle - and grow the Apollonian packing.

Math

The isoperimetric problem

One cord of fixed length on pins: add sides and watch the enclosed area grow toward the circle's while a ruler shows the cord is still the same length; then predict which of two shapes from the same cord holds more, and check.