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Tag Archives: square
Book review: Tales of Impossibility
[Disclosure of Material Connection: Princeton Press kindly provided me with a free review copy of this book. I was not required to write a positive review. The opinions expressed are my own.] Tales of Impossibility: The 2000Year Quest to Solve … Continue reading
Posted in books, review
Tagged algebra, antiquity, circle, constructible, construction, cube, geometry, impossibility, polygon, problems, square, tales, trisect
4 Comments
The route puzzle
While poking around some old files I came across this puzzle: (Click for a larger version.) I didn’t make it, and I have no idea where I got it from (do you know?). But in any case, wherever it comes … Continue reading
Posted in arithmetic, challenges, number theory, proof, puzzles
Tagged cube, perfect, prime, puzzle, route, square, triangular
7 Comments
Golden numbers are Fibonacci
This post is fourth in a series, proving the curious fact that is a Fibonacci number if and only if one (or both) of or is a perfect square; we call numbers of this form golden numbers. Last time, I … Continue reading
Posted in arithmetic, computation, famous numbers, fibonacci, proof
Tagged Cassini, fibonacci, formula, lucas, square, test
2 Comments
Fibonacci numbers are golden
Recall that a “golden number” (this is not standard terminology) is a number such that one (or both) of or is a perfect square. In this post, I’ll explain Gessel’s proof that every Fibonacci number is golden. First, we need … Continue reading
Posted in arithmetic, computation, famous numbers, fibonacci, proof
Tagged Cassini, fibonacci, formula, lucas, square, test
1 Comment
Testing Fibonacci numbers: the proofs
In my last post I stated this surprising theorem: is a Fibonacci number if and only if one of is a perfect square. If one of is a perfect square, then let’s say that is a “golden number” (a nod, … Continue reading
Posted in arithmetic, computation, famous numbers, fibonacci, proof
Tagged fibonacci, formula, square, test
1 Comment
Testing Fibonacci numbers
From a recent post on Brian Hayes’ blog, bitplayer, I learned the following curious fact: is a Fibonacci number if and only if either or is a perfect square. Recall that the Fibonacci numbers begin where each number is the … Continue reading
Posted in arithmetic, computation, famous numbers, fibonacci
Tagged fibonacci, formula, square, test
8 Comments
A selfsquare number
[This is the seventh in a series of posts on the decadic numbers (previous posts: A curiosity, An invitation to a funny number system, What does “close to” mean?, The decadic metric, Infinite decadic numbers, More fun with infinite decadic … Continue reading
Posted in arithmetic, infinity, iteration, modular arithmetic, proof
Tagged decadic, idempotent, self, square
12 Comments