Fibonacci Flim-Flam. The Fibonacci Series Leonardo of Pisa (~1170-1250), also known as Fibonacci, wrote books of problems in mathematics, but is best known by laypersons for the sequence of numbers that carries his name: This sequence is constructed by choosing the first two numbers (the "seeds" of the sequence) then assigning the rest by the rule that each number be the sum of the two preceding numbers. This simple rule generates a sequence of numbers having many surprising properties, of which we list but a few: Take any three adjacent numbers in the sequence, square the middle number, multiply the first and third numbers.
The Fibonacci sequence is but one example of many sequences with simple recursion relations. The Fibonacci sequence obeys the recursion relation P(n) = P(n-1) + P(n-2). A striking feature of this sequence is that the reciprocal of f is 0.6180339887... which is f - 1. The ratio f = 1.6180339887... is called the "golden ratio" or "golden mean". Fibonacci Foolishness. Golden Spiral Hype. Math Monday – The Squared Square – The Museum of Mathematics. Math Monday: The Squared Square by George Hart If you’re a cabinet maker, geometry is essential to all of the lengths and angles that you calculate. The cabinet shown here goes further and presents the solution to a rather difficult dissection problem. This is the simplest perfect squared square. The entire area is a square and it is divided into squares of distinct integer sizes.
There are twenty one different squares, with the sizes indicated below, covering a 112 by 112 area. Taking this solution and turning it into a beautiful piece of furniture was the work of Bob Mackay. Math-ish question. I'm in the process of building a Jerry Andrus-like "impossible object" that I've designed, and I've run into a snag with the shape of one of the pieces. I'm hoping someone more math-oriented than me here could help me with it. The piece is best described like this. Picture a rectangular box. The top and bottom are squares, so the width and depth are equal: Now picture two lines: one running from top to bottom along the inner right edge; and the other forming a diagonal, from the inner top left corner to the outer bottom right corner (the front and right faces of the box are removed for clarity): What I'm interested in is the curved surface bound by those two lines: Specifically, I'm trying to figure out how to map this 3-d shape onto a 2-d surface -- in other words, I want to figure out what shape I would need to cut a flat piece of paper into, so that when it was twisted it would form the above shape.
To help figure this out, I've made a few rough models like this: 1. 2. 3. 4. 5. 6. 7. 1. 50 Best Mathematics Blogs. Arthur Benjamin does "Mathemagic". Moebius (Möbius) strip in art and culture | Imaging and a little bit of OSS. In 1858, two German mathematicians, August Ferdinand Möbius and Johann Benedict Listing, independently discovered what is popularly known as the Möbius strip.
The characteristic feature of Möbius strip is that it is a surface with single side. In its most simplest form a Moebius strip can be constructed out a a strip of paper which is twisted halfway and the ends joined together. If one were to start tracing a surface, by the time they complete one trace they find that they are tracing the opposite side of the paper than the one from which they started. Go another round and you come back to the same side. Basic Moebius strip (twisted ribbon) A Mobius strip can be expressed mathematically in several diffferent forms. X(u,v) = cos(u) + v*cos(u/2)*cos(u) y(u,v) = sin(u) + v*cos(u/2)*sin(u) z(u,v) = v * sin(u/2) Default values for u and v: u = [0, 2π] for one complete loop;, v = [-0.4, 0.4] Rendering of Moebius strip using Matlab M. M. Moebius Strip written onto a transparent Moebius Strip. MathematicalPi. Who Can Name the Bigger Number?
[This essay in Spanish][This essay in French] In an old joke, two noblemen vie to name the bigger number. The first, after ruminating for hours, triumphantly announces "Eighty-three! " The second, mightily impressed, replies "You win. " A biggest number contest is clearly pointless when the contestants take turns. But what if the contestants write down their numbers simultaneously, neither aware of the other’s? To introduce a talk on "Big Numbers," I invite two audience volunteers to try exactly this. So contestants can’t say "the number of sand grains in the Sahara," because sand drifts in and out of the Sahara regularly. Are you ready? The contest’s results are never quite what I’d hope. And yet the girl’s number could have been much bigger still, had she stacked the mighty exponential more than once. . , for example. Or Place value, exponentials, stacked exponentials: each can express boundlessly big numbers, and in this sense they’re all equivalent. .) .
As much as the latter exceeds 9.