👉 Spider math, also known as the "spider equation" or "spider number theorem," is a mathematical concept that involves a simple yet intriguing relationship between the number of spiders and the distances they travel. It posits that if a spider starts at one location and moves in a straight line to a point 3 units away, then from that new position, it can move 1 unit to the right and 2 units up, and so on, forming a sequence of right-angle triangles. The total distance the spider travels forms a right triangle where the legs are 3 and 1 (the initial 3 units plus the subsequent 2 units), and the hypotenuse represents the total distance from the starting point to the furthest point reached. This sequence of distances (3, 4, 5, 6, 7, 8,...) follows the pattern of triangular numbers, which are the sums of consecutive integers starting from 1. The nth triangular number is given by the formula \( T_n = \frac{n(n+1)}{2} \), illustrating how the spider's path grows in a predictable, geometric manner.
