Puzzle o' the Day 409!
I've been obsessed lately with Euclidea, an app that turns compass-and-straightedge constructions into puzzles. Here's a puzzle inspired by Euclidea.
Recall that in compass-and-straightedge constructions, there are two basic moves:
(1) Draw a circle, given its center and a point on its circumference.
(2) Draw a straight line through two given points.
a.i. (Medium-easy). You're given a line l and a point P on l. Your challenge: draw a line perpendicular to l that goes through P. The "standard" way to do so (that is, the one taught in most Geometry classes) involves four moves. Can you find and/or remember it?
Hint (in white): The solution depends on the classic perpendicular bisector construction.
Hint (in white): The sequence of moves is circle-circle-circle-line.
a.ii. (The puzzle: medium without the hints, medium-easy with). Can you find a construction that requires only *three* moves?
Hint (in white): The solution is dependent on Thales' Theorem; the Wikipedia article on it can be found here.
Hint (in white): The sequence of moves is circle-line-line.
b.i. (Medium-easy). You're given a line l and a point P not on l. Your challenge: draw a line perpendicular to l that goes through P. Can you find and/or remember the four-move solution?
Hint (in white): The solution depends on the classic perpendicular bisector construction.
Hint (in white): The sequence of moves is circle-circle-circle-line.
b.ii. (Medium without the hints, medium-easy with). Can you find a construction that requires only *three* moves?
Hint (in white): The solution relies on symmetry.
Hint (in white): The sequence of moves is circle-circle-line.
Recall that in compass-and-straightedge constructions, there are two basic moves:
(1) Draw a circle, given its center and a point on its circumference.
(2) Draw a straight line through two given points.
a.i. (Medium-easy). You're given a line l and a point P on l. Your challenge: draw a line perpendicular to l that goes through P. The "standard" way to do so (that is, the one taught in most Geometry classes) involves four moves. Can you find and/or remember it?
Hint (in white): The solution depends on the classic perpendicular bisector construction.
Hint (in white): The sequence of moves is circle-circle-circle-line.
a.ii. (The puzzle: medium without the hints, medium-easy with). Can you find a construction that requires only *three* moves?
Hint (in white): The solution is dependent on Thales' Theorem; the Wikipedia article on it can be found here.
Hint (in white): The sequence of moves is circle-line-line.
b.i. (Medium-easy). You're given a line l and a point P not on l. Your challenge: draw a line perpendicular to l that goes through P. Can you find and/or remember the four-move solution?
Hint (in white): The solution depends on the classic perpendicular bisector construction.
Hint (in white): The sequence of moves is circle-circle-circle-line.
b.ii. (Medium without the hints, medium-easy with). Can you find a construction that requires only *three* moves?
Hint (in white): The solution relies on symmetry.
Hint (in white): The sequence of moves is circle-circle-line.