A Curious Pattern Indeed
A teaser for some future videos regarding a pattern which lures an unsuspecting doodler into thinking it will be powers of two.
==========
3Blue1Brown - "A Curious Pattern Indeed" [CC by Yuval Dolev] Pick two points on a circle, and draw a line straight through. The space which was encircled Is divided into two. To this point add a third one, which gives us two more chords. The space through which this lines run, has been fissured into four. Continue with a fourth point, and three more lines drawn straight, Now the count of disjoint regions, sums, in all, to eight. A fifth point and its four lines, support this pattern glean, Counting sections, one divines, that there are now sixteen. This pattern here of doubling, does seem a sturdy one, But one more step is troubling, as the sixth gives thirty-one. Wait.. what? 1, 2, 4, 8, 16, ... 31? What's going on here? Why does the pattern start off as powers of two, Only to fall short by one at th...
==========
3Blue1Brown - "A Curious Pattern Indeed" [CC by Yuval Dolev] Pick two points on a circle, and draw a line straight through. The space which was encircled Is divided into two. To this point add a third one, which gives us two more chords. The space through which this lines run, has been fissured into four. Continue with a fourth point, and three more lines drawn straight, Now the count of disjoint regions, sums, in all, to eight. A fifth point and its four lines, support this pattern glean, Counting sections, one divines, that there are now sixteen. This pattern here of doubling, does seem a sturdy one, But one more step is troubling, as the sixth gives thirty-one. Wait.. what? 1, 2, 4, 8, 16, ... 31? What's going on here? Why does the pattern start off as powers of two, Only to fall short by one at th...
