# Final Scene - Placement of the Pins

TLDR - I found the distance between the pins using the formula for equilateral triangles.

I took a slightly different route to figuring out the spacing between the pins. In following the lecture, the spacing between the pins roughly equates to 30cm (or 3 BUs). That being said, the bowling pins’ positions form equilateral triangles.

So in order for the pins to remain exactly 3 BUs apart, we have a bit of math to do. If the distance between each pin is 3 BUs, that means that the distance between each row of pins (the height of the equilateral triangle) is the square root of 3, divided by 2, multiplied by x, where x is the distance between the pins (so x = 3). This equates to 2.598 (2.6 is what I rounded to for my placement). If we consider that Pin 1 is at the origin (0,0) on a grid, that pin 2 and 3 would be at (-1.5, 2.6) and (1.5, 2.6) respectively

On the flip side, if you follow the placement of the pins, based on the video, the distance between the first and 2nd set of pins is actually ~3.354 and not 3. This is proved through the Distance Formula (see Resources below.)

Here’s a screenshot to show the differences in placement. My proof is on the left, and the lecture’s proof is on the right.

Resources:

http://www.mathwarehouse.com/algebra/distance_formula/index.php