count-table
Bézout's number, and the answer
3 polynomial systems, each solved by tracking every one of Bézout's paths. The Bézout column is what the *shape* of the system permits; the solutions column is what it has. four-bar coupler pin: 4 → 2; 3-RPR platform: 16 → 6; Burmester, five poses: 16 → 4. The last column is how many paths were tracked per solution found.
How many answerswide
Where it is used
- Following a root from a problem already solved How many answers
- The paths that leave How many answers
- The count that does not move How many answers
- Eight ways to hold the same tool One path to the tool
- Five positions, and what is left The problem backwards
- Twenty-eight, not forty How many answers
- The search that was right How many answers
- Two to the power of the dyads How many answers
- Four that a compass cannot reach The chain before the lengths
- How many points may be prescribed The problem backwards
- A degree counted on a line How many answers
- The curve nobody eliminates How many answers
- Nine times through each circular point How many answers
- Every rational gear ratio has a degree How many answers
- The mesh inside keeps the half How many answers
- Branches were components all along One path to the tool
- Where a slide puts the rest of the degree How many answers
- The double points that leave for infinity How many answers
- The double point a slide cannot keep How many answers
- The trammel takes both double points How many answers
- A four-bar becomes a trammel along a family of laws How many answers
- Three discs decide the real double points How many answers
- A growing four-bar reaches none of its departing double points How many answers
All essaysFieldsThreadsLaddersThe mechanism ledgerRefutationsConceptsSearch