# Tag Archives: double

## Efficiency of repeated squaring: another proof

In my previous post I proved that the “binary algorithm” (corresponding to the binary expansion of a number ) is the most efficient way to build using only doubling and incrementing steps. Today I want to explain another nice proof, … Continue reading

Posted in computation, proof | | 3 Comments

## Efficiency of repeated squaring: proof

My last post proposed a claim: The binary algorithm is the most efficient way to build using only doubling and incrementing steps. That is, any other way to build by doubling and incrementing uses an equal or greater number of … Continue reading

Posted in computation, proof | | 2 Comments

## Efficiency of repeated squaring

As you probably realized if you read both, my recent post without words connects directly to my previous post on exponentiation by repeated squaring Each section shows the sequence of operations used by the repeated squaring algorithm to build up … Continue reading

Posted in computation | | 7 Comments

## A new way to read (and print) double-sided paper

Continuing with the theme of reading stacks of paper (see my previous two posts, I have had a marvellous idea (at least I think so; I will let you judge for yourself). Let me take you through my thought process, … Continue reading

Posted in pattern, solutions | Tagged , , , , , | 11 Comments

## Reading double- and triple-sided paper

In the comments on my previous post there are some nice suggested algorithms for reading a stack of double-sided sheets of paper. The key seems to be that you need to keep track of a distinguished edge of the stack. … Continue reading

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## John Conway’s algorithms for counting stairs and reading double-sided paper?

This past week I started reading Siobhan Roberts’s new biography of John Conway, Genius at Play: The Curious Mind of John Horton Conway. I’m enjoying it so far. I’ll have more to say about it later, once I finish it, … Continue reading

Posted in Uncategorized | Tagged , , , , , | 9 Comments