05 August 2011

One and a half versus the square root of two

After looking at diagonal movement on a square grid, I started wondering how far a figure would need to move before the difference between 32 and the √2 square root of two became significant. (Simple curiosity here. Nothing more.)

What amount of error is significant? 12? 1? 32?

Let’s go with 1. Check my math: (sqrt(2) * x) + 1 = 1.5 * x

It turns out x is about 12. Here’s my check: (1.5 * x) - (sqrt(2) * x); x = 12 which yields a result just a little over 1.

That’s smaller than I was expecting. Though it is still reasonable for most games. A twelve square per turn movement rate will start to get problematic for other reasons.

2 comments:

Aaron E. Steele said...

If you give your typical human a move of 6" per turn, you can minimize any problems

anarchist said...

Hi,

Apologies for the off-topic comment, but I couldn't find a contact email for you.

I've recently put out an ebook of my writing, called 'The New Death and others'. It's mostly short stories, with some obvious gamer-interest material. For example I have a story inspired by OD&D elves, as well as poems which retell Robert E Howard's King Kull story 'The Mirrors of Tuzun Thune' and HP Lovecraft's 'Under the Pyramids'.

I was wondering if you'd be interested in doing a review on your blog.

If so, please let me know your email, and what file format is easiest for you, and I'll send you a free copy. You can email me (news@apolitical.info) or reply to this thread.

You can download a sample from the ebook's page on Smashwords:

http://www.smashwords.com/books/view/92126

I'll also link to your review from my blog.

Yours,
James.