6 ms·
Folding fractions
- allthatglitters 12y agoThe is a delightfully entertaining article! Does anyone have a recommendation on the Kazuo Haga book, "Origamics"? vs David Mitchell's "Paper Crystals"? Origamics is a bit pricey... worth it?
- GregBuchholz 12y agoFor books of questionable worth, I like to go to my local library, and get an interlibrary loan. I find this indispensable for mathy books, where it can be hard to judge the necessary prerequisites.
- raimondious 12y agoOrigamics is a wonderful book, it is worth it if you are interested in math or origami.
- Avitas 12y agoThis is one of those interesting items that is truly deserving of the headline "Neat Trick." It reminds me of a card trick that I learned as a child that appeared to work by magic, but instead worked every time because it involved something complex going on involving math.
- dsjoerg 12y agoRuler Manufacturers Hate Him!
- GregBuchholz 12y agoIt seems like the link to the book is broken. Origamics: Mathematical Explorations Through Paper Folding https://books.google.com/books?id=zJR2Rr_wuFQC https://books.google.com/books?id=zJR2Rr_wuFQC
- murbard2 12y agoFolding a third is not nearly as impressive as angle trisection, which is impossible with a straight ruler and compass, but possible using origami. http://en.wikipedia.org/wiki/Angle_trisection#Using_origami http://en.wikipedia.org/wiki/Angle_trisection#Using_origami
- cbd1984 12y ago> angle trisection, which is impossible with a straight ruler and compass To be clearer: It is impossible to come up with a general algorithm to exactly trisect an arbitrary angle using only a straightedge (not a ruler) and a compass in a finite number of steps. And the straightedge isn't a ruler because it can't be used to measure distances. Neither can the compass. This is an axiom system, and therefore the rules are absolute. http://en.wikipedia.org/wiki/Compass-and-straightedge_construction http://en.wikipedia.org/wiki/Compass-and-straightedge_constr...
- murbard2 12y agoYes, I meant straight edge, sorry I had an ESL moment.
- pbhjpbhj 12y agoYou're not wrong per se - a ruler usually has graduations but _could_ just be a straight-edge. However, as the GP says, "ruler" implies a straight-edged measuring stick (aka "measure" [n]). Ruler derives, I gather, from Latin regula which just means a straight stick or bar and in turn derives from terms referring to keeping straight (literally or figuratively). tl;dr measuring stick ⊂ ruler.
- murbard2 12y agoMy native tongue is French, where it is "règle et compas", I translated règle tu ruler, but added straight in front vaguely remembering that the English expression had the word "straight" in it.
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- dmayle 12y agoThis is really useful for origami, when you want to fold unusual splits into your paper. You can also use it in the opposite direction, so instead of bringing the point up to a specific mark on the top edge going from left to right (e.g. 1/2 on top gets you 2/3 on the right that you divide in two to get 1/3), you plan it so that your right edge get's crossed at 2/n (e.g. fold the paper so that the y length is 1/2, then your point will hit the 1/3 mark at the top of the paper). This is useful when you want to go from an easy fraction like 1/8 to 1/7, as opposed to going from 1/4 through 1/5 and 1/6 to get to 1/7.
- hammock 12y agoAlways wondered how to do this and never figured out how. My solution was to roll up the paper into a circle and slowly crease at the right roll amount. Reminds me of my old compass and straight edge lessons...
- deleted 12y ago[deleted]
- Avshalom 12y agoThere's an easier way to do this by the way: Fold an arbitrary length perpendicular to the axis you want, then fold that length again... To X folds. Fold diagonally from top corner to the last fold then fold at the the intersections. ___ ___ ___ _____ | | |___| |__/| |_|_|/| | | |___| |_/_| |_|/|_| | | |___| |/__| |/|_|_| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |___| |___| |___| |_|_|_|
- deleted 12y ago[deleted]
- chris_wot 12y agoI love using doing things like this. Possibly somewhat off-topic, but the proof for the equation sin(A + B) = sin A.cos B + cos B.sin X is quite a nifty diagram that can be found here: http://en.wikipedia.org/wiki/List_of_trigonometric_identities#mediaviewer/File:AngleAdditionDiagramSine.svg http://en.wikipedia.org/wiki/List_of_trigonometric_identitie...
- amelius 12y agoInteresting. But, it must be said that he was just lucky that the x^2 terms canceled :)