Mathematics · the experiment
Untangle the complete graph
Every pair of dots is joined by a segment. Drag the dots to undo the crossings, then redo the counts of the proof.
1 · Untangle five dots
Beginner
According to the article, how many crossings must you accept at the very least with 5 dots?
Drag the dots so that as few crossings as possible remain.
2 · Move on to six dots
Intermediate
Delete each of the 6 dots in turn. Every leftover 5-dot drawing has at least 1 crossing, and each crossing survives exactly 2 of the 6 deletions. What follows?
Six dots, starting from a circle: drag them down to the minimum. A lead: three inside, three outside.
3 · Count for eight dots
Expert
Same reasoning with 8 dots: each of the 8 leftover 7-dot drawings has at least 9 crossings. How many crossings at least with 8 dots?
4 · Take away one curve
Expert
With 8 dots, the article gives at least 18 crossings, and 15 without one curve. In an 8-dot drawing with 18 crossings, how many crossings can a single curve carry?
Your 6-dot drawing is back. Tap a curve to take it away, then go down to the minimum.
Graph untangled
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