One of the gems from our mathematical ancestors, equal to the divinity of the Phi Ratio.
Here are 2 unique methods to generate a precise 3-4-5 Triangle inside a 5x5 unit Grid.
Method 1: Using only 3 Straight Lines:
(extracted from Robert Lawlor’s classic book: “Sacred Geometry”).
Draw a 5x5 Grid, and mark the midpoint of 2 sides, the vertical side on the right, and the horizontal edge at the bottom. Draw 3 straight diagonal lines: the first line going from the top left corner and proceeding to the midpoint of the base line, and the second line intersecting this, as it travels from the bottom left corner to the midpoint and going to the midpoint of the right-hand vertical side. Where they intersect at 90 degrees gives us the critical point how to construct the 3-4-5 Triangle. This gives the obvious 3rd diagonal that also travels from the top left corner to the midpoint of the right-hand side vertical. If we consider this 5x5 Square to be the Unit Square of 1x1, then the length of both these straight lines, that intersected, have a length of Root 5 divided by 2 = 1.118... This revelation of Root 5, is a clue to the next demonstration that shows there exists a Golden Phi relationship inside the 3-4-5 Triangle, when a specific circle is constructed. This is because the formula for Phi is (1 + Root 5)/2. Also 1.118… is related to the gap between the dynamics of the Square in the Circle. We can conclude that the 3-4-5 Triangle is intimately connected the Living Mathematics of Nature as expressed by Phi and Root 5.
Jain 108
