cliomancer:vanquishedvaliant: krystal-prisms:genericaura:genericaura:jehomovah:indefinite-free-pizza
cliomancer:vanquishedvaliant: krystal-prisms:genericaura:genericaura:jehomovah:indefinite-free-pizza: Fun fact! Because of how grid measurements work in dnd, this doesn’t actually work! The Pythagorean Theorem in D&D actually ends up equivalent to c = greater(a : b). This also means that a circle in D&D has more than 360 degrees, and pi is a larger number. This also explains why ball-and-chain weapons are more prevalent in D&D settings, as centripetal force is calculated partly based on pi and thus they would have more force when swung. @indefinite-free-pizza wait wait How do the grid measurements in DnD break the Pythagorean theorem? I’m on board with all these other causal effects of that if it’s true but why is it true Rules as written, moving diagonally still takes 5 feet. So if I wanted to walk 10 feet north and 10 feet east, that would be 20 feet but I could also just walk diagonally and do it in 10. Now let’s apply this to a circle. I’ll mark 8 points 10 feet away from a point and we can guess from there where the circumference is.I walk north, south, east, and west 10 feet and mark it just fine. But then it gets weird when I use my movement to go northeast, northwest, southeast, and southwest. Because now it’s a square. But I’m still equidistant from the middle so it’s a circle.To prove the above that c = greater (a:b) let’s use two different numbers. I want to end up 20 feet north and 10 feet east. To start, I’m going to be efficient and move 5 feet diagonally, and then do that again. Now I’m as far east as I need to be but not north enough so I move north another 10 feet. 10 feet diagonally + 10 due north means this triangle has two 20 foot sides, a 10 foot side, and a right angle.Using the variant rule of every other diagonal movement costs 10 feet brings us closer to real life, but it’s not quite right, especially below 15 feet. Then the pythagorean formula becomes c=greater(a:b) + ( lesser(a:b)/2 rounded down). Just got home so here’s some diagrams to help visualize these math crimes. Also, I just thought of a really good line to end this on. In DnD, you can literally fit a square peg into a round hole. Dnd broke math The “Variant” rule for alternating 10 feet was the standard prior to 5th edition and was omitted for presumably simplicity, since 5th has an almost callous disregard for the existence of its grid system and likes to pretend it doesn’t exist whenever possible. That said; true circles are not in fact calculated this way even in 5th edition as you do measure effects that are intend to be measured in circles or spheres as circles and spheres, and they don’t skip range on the corners.If anything this suggests less that the rules of spherical physics and pi in 5th edition DND are broken, but merely that living (or animate) creatures specifically can locomote at a comically accelerated speed upon a diagonal axis, but otherwise slow down when moving cardinally to… presumably the plane’s magnetic poles?It’s worth noting that 5th edition DND is not even close to a world simulation anymore like some earlier editions attempted, and frequently eschews ruling in favor of gameplay simplicity, this no less the case…However, I’m extremely intrigued by the implications on travel accommodations, trade, and the structure of nations and the world if those people truly are able to move faster diagonally.How would cities be founded when you can travel more quickly moving Northeast than simply North or East? Most nations are theocracies because Bishops can move 41% faster than the nearest equivalent force. -- source link