Comments on: Interesting approximations using trigonometry

By: Prasad Kulkarni

Prasad Kulkarni — Mon, 07 Mar 2011 05:51:15 +0000

Awesome.. You guys really doing some good approximation and bringing some fun to it. How I wish Twitter had been there in my school days.

By: Approximations with continued fractions « Alasdair's musings

Approximations with continued fractions « Alasdair's musings — Sat, 05 Jun 2010 00:39:02 +0000

[...] with continued fractions Posted on June 5, 2010 by amca01 In an excellent blog post earlier this year, Dave Richeson commented on the [...]

By: Dave Richeson

Dave Richeson — Wed, 24 Feb 2010 13:51:23 +0000

Wow, good eyes. Thank you for catching that. I updated the post.

By: Walt

Walt — Wed, 24 Feb 2010 13:06:47 +0000

Found a small typo in your typesetting: the CF of pi is 3; 7, 15, 1, 292 – you forgot the 1 after the 15 in your nested fraction.

By: The math behind a neat calculator trick « Division by Zero

The math behind a neat calculator trick « Division by Zero — Thu, 18 Feb 2010 01:50:32 +0000

[...] math behind a neat calculator trick I received an interesting comment on yesterday’s blog post from Nemo. It was a cool calculator trick that I’d never seen before. Nemo wrote: Reminds me [...]

By: Dave Richeson

Dave Richeson — Wed, 17 Feb 2010 19:38:07 +0000

Excellent, I’d never seen that before! Good use of and the radians-to-degrees conversion. I’ll have to show that to my students.

By: Nemo

Nemo — Wed, 17 Feb 2010 19:27:31 +0000

Reminds me of my favorite calculator trick.

Set your calculator to degrees mode (NOT radians).

Type in a bunch of 5′s: 555555, or whatever.

Press “1/x”.

Press “sin”.

Examine the mantissa of the result. Magic!

By: Dave Richeson

Dave Richeson — Wed, 17 Feb 2010 15:06:22 +0000

John,
Thanks for pointing that out. I did notice that some approximations were better than others, but hadn’t thought about why.

Dave

By: John

John — Wed, 17 Feb 2010 04:17:45 +0000

That’s great! You really ran with this.

One footnote: Good approximations to pi lead to great approximations to 1 when you take sines. Taylor series says sin(pi/2 + h) is approximately 1 – 0.5 h^2 for small h. So the error in the approximation for pi gets squared.