Recently in mathematics Category

For those who put the month before the day (why?), today is 3/14: Pi day.

So happy Pi day! Have some pi:

let p d = take d(fix(\i y h->let(z,x)=fix(\f xs->case xs of{((n,d,c):y)->let{(z,k)=f
y;(q,r)=(c*10+k)`divMod`d}in((n,d,r):z,n*q);_->([],0)})y in case x of{9->i z(h++[9])
10->i z(map(\x->(x+1)`mod`10)h++[0]);_->h++i z[x]})((1,10,2):[(i,2*i+1,2)
|i<-[1..(10*d)`div`3]])[])in p 100

Feel free to change the "100" at the end to however much precision you need.

The proof is left as an exercise.

Lambdacats is the Haskell rendering of an Internet meme, lolcats. I did a few of them, but several didn't make it to arcanux, on the grounds that they're too much of an in-joke. I can respect that.

This one isn't Haskell-specific, but it is based on a perennial Haskell discussion: The efficient computation of Fibonacci numbers.

So without further ado...

Original photograph by MyRabbits

Over at Lard Bucket, Andy Schmitz looks at Adi Shamir's secret sharing method. He identifies what he considers a possible flaw in the method, using an example from the Wikipedia entry, and invites readers to critique his reasoning.

The executive summary: Andy's reasoning is 100% correct, and so is Shamir's assertion (in the paper) that the method does not leak information.

Read on for details.

This is part of a series. You may like to read part 1 and part 2 first.

In this part, we look at how to extend integration of polynomials to fancier expressions.

The second part in a series. You may wish to read part 1 first.

In this action-packed episode, we go through some of the theory that we need to understand integration algebraically.

Well, time to show my true geekiness with a series. We're going to do symbolic integration. You know, anti-derivatives.