gadget
the reflector, solved
A rhombus whose far vertex is held on a line through the pivot. One side is the input, the line is the mirror, and the other side comes out reflected in it — which is where negation, doubling and addition all come from. The relation it satisfies is (μ, θ) ↦ 2μ − θ, and across a sweep of 41 positions the worst departure from it is 1.3e-13 radians. Every joint here is the output of a Newton–Raphson solve on the bar lengths; nothing is placed by the formula the picture is about.
The curve as an equationdraggable: input anglewide
Where it is used
- Four bars that add two angles The curve as an equation
- A parallelogram carries an angle, and only so far The curve as an equation
- Doubling is cheaper than adding The curve as an equation
- The machine, compiled The curve as an equation
- The proof drew more than the curve The curve as an equation
- A bar between two midpoints The curve as an equation
- Where the machine stops being the function The curve as an equation
All essaysFieldsThreadsLaddersThe mechanism ledgerRefutationsConceptsSearch