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Although this archeological find relates to Pythagorean Triples, my take is that one of the most basic concepts in carpentry, the "3-4-5" rule for finding right

Although this archeological find relates to Pythagorean Triples, my take is that one of the most basic concepts in carpentry, the "3-4-5" rule for finding right angles, which is described by Euclid and is certainly related to the Pythagorean theorum, now would logically seem to have been used much earlier. The 3-4-5 rule holds that a right angle is deduced by marking 3 equal units on the x axis, then drawing a wide arc of 4 of the same units somewhat orthogonally (appearing to go both plus and minus) from point 0 of the x axis, then marking the point from the top of the x axis to the point on the arc at which the gap is exactly 5 of the same units. The result is a right angle. By using a plumb bob to create a vertical x axis in the first place, the resulting y axis is thus horizontal. The 3-4-5 rule is and was essential in structural work, so I'm suggesting that meaningful contributions to architecture and other pursuits were made using the 3-4-5 rule long before the use of trigonometry as we know it from Pythagorus, so any move of the Pythagorean Triples timeframe would thus apply to the timeframe of the 3-4-5 rule. I hope someone will correct any errors/delusions in my summary.

CheezeIt 5y ago
Maybe they just used a square (tool) or levels. Geometrically the simpler and more precise way to make a perpendicular line is to mark two points an equal distance on the left and right, and then from them intersect circles of a larger radius above the line. Drop a perpendicular down to your starting point. That’s much more precise because you don’t need to have a radius 5/4 the size of another one. But you can lay out rectangles on the ground with proper right angles with fewer workers if you use the Pythagorean theorem instead of trying to get a parallelogram out of ropes with the diagonals equal.
- cf100clunk 5y ago
  Creating a square tool required some sort of rule or trick: the 3-4-5 rule, your solution, or blind luck. Creating a level meant easily deducing a straight line from the surface of a liquid, which became known as a "spirit level". The 3-4-5 rule was also easy to use with tools such as calipers, protractors, and lengths of cord. Also, from the standpoint of working in enclosed spaces, the 3-4-5 rule takes about half the width of your solution.

CheezeIt 5y ago

Maybe they just used a square (tool) or levels. Geometrically the simpler and more precise way to make a perpendicular line is to mark two points an equal distance on the left and right, and then from them intersect circles of a larger radius above the line. Drop a perpendicular down to your starting point. That’s much more precise because you don’t need to have a radius 5/4 the size of another one. But you can lay out rectangles on the ground with proper right angles with fewer workers if you use the Pythagorean theorem instead of trying to get a parallelogram out of ropes with the diagonals equal.

cf100clunk 5y ago
Creating a square tool required some sort of rule or trick: the 3-4-5 rule, your solution, or blind luck. Creating a level meant easily deducing a straight line from the surface of a liquid, which became known as a "spirit level". The 3-4-5 rule was also easy to use with tools such as calipers, protractors, and lengths of cord. Also, from the standpoint of working in enclosed spaces, the 3-4-5 rule takes about half the width of your solution.