What is Pythagoras’ Theorem?
We’re glad you asked! Pythagoras’ Theorem, also called the Pythagorean Theorem, is a geometry formula discovered by the ancient Greek mathematician Pythagoras sometime between 569 – 475 BC. The theorem states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides. In other words, if a triangle has a right angle (90°), and you make a square on each of the three sides, then the biggest square has the exact same area as the other two squares combined.
The formula is typically written as a short-form equation that relates the lengths of sides a, b, and c together.
Today, various industries use Pythagoras’ Theorem, including surveying, 2D navigation, architecture, and of course, rigging and construction. In rigging, the most common use for Pythagoras’ Theorem is determining a sling length based on distance, available headroom, or available gear.
Using the formula to determine sling length or headroom typically applies to applications using spreader beams. However, you may also use the formula to help assess rigging options when a load’s center of gravity (CG) is known, but there’s a finite amount of space above.
To see Pythagoras’ Theorem in action, calculating headroom for a typical crane lift utilizing spreader beams, check out How Much Headroom Do I Need (Part 2).
Additionally, the theorem may play a part in determining sling capacity based on tension. This relates to finding either the sling length or headroom (whichever factor is unknown), then calculating the tension factor (TF) to determine the actual load seen by the sling. This determination is useful in deciding whether the sling you have on-site is sufficient for the load.
To sum it up, knowing and applying Pythagoras’ Theorem can help in various rigging applications when it comes to determining and/or understanding headroom, sling length, sling tension, and load angle factors.
Below are some equations you can use to get started finding the unknown side of a right-angle triangle, courtesy of the Jerry Klinke Rigging Handbook, 5th Edition.