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Constructing a Four-Point Egg
- heckelson 3y agoGreat egg. Thanks for posting
- deleted 3y ago[deleted]
- dr_kiszonka 3y agoOne free tool for making such diagrams is GeoGebra. Online: https://www.geogebra.org/geometry https://www.geogebra.org/geometry Offline: https://www.geogebra.org/download https://www.geogebra.org/download (I have no affiliation with it. It was used in an article OP's submission links to.)
- danbruc 3y agoYou can also try paper, pencil, ruler and compass.
- hughes 3y agoYou can try a bit of burnt wood and a cave wall.
- lapetitejort 3y agoYou can use a stick and some dirt, as long as no Macedonian kings block your sun
- shashanoid 3y ago[flagged]
- blt 3y agowow, apparently this comment touched a nerve
- dylan604 3y agoDo schools even teach paper/pencil/ruler/compass any more? I get not teaching slide rule, but using a straight edge and compass is even older than slide rule. I actually enjoyed drawing things like this, but I know that's not something all do. I can easily see where this is something lost with CAD and other graphing apps.
- lupire 3y agoYes, but they use a "non-collapsing" compass that can transmit distances without constructing them, not Euclid's compass (which can be used to transmit distances, with more work). http://euclidea.xyz http://euclidea.xyz
- dylan604 3y agoI like how you responded to a question about not using apps with an app.
- an_aparallel 3y agoi have this mechanical drafting book - it's fucking amazing. Goes from simple euclidean type stuff - all the way to full parts, amazing patterns and so on: https://www.amazon.com.au/Popular-Mechanics-Art-Mechanical-Drawing/dp/1588167593 https://www.amazon.com.au/Popular-Mechanics-Art-Mechanical-D...
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- kbelder 3y agoThat's important, I think... not just historically, but to assist in concept formation. Although, replace 'ruler' with 'straightedge', to emphasize that there is no measuring.
- danbruc 3y agoI choose ruler over straightedge because that is what people will have more commonly and you can always ignore the scale.
- shashanoid 3y agoThanks having fun on geogebra
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- rantallion 3y agoWhat makes this a four-point egg if only the first three points are required to derive the rest of the shape?
- burkaman 3y agoSee Figure 15 on page 8: https://web.archive.org/web/20200618202007/https://www.dynamat.oriw.eu/upload_pdf/20121022_154322__0.pdf https://web.archive.org/web/20200618202007/https://www.dynam... The egg is constructed of four distinct arcs based on four different points, plus two of them mirrored.
- rantallion 3y agoThanks. This makes more sense. I was curious why the _inner_ point mattered, when the fourth point is actually the one on the side.
- eduhetxub 3y agoI don't know exactly what you mean, but the name of this shape is consistent with the naming of traditional geometric constructions like the "five-centered arch" and the "three-centered arch" (see many diagrams online for details of these constructions). So "four-centered egg" might make more sense to you, though it could also be called the "six-centered egg", because it includes both sides, unlike the classical arch constructions.
- a_t48 3y agoThere are four points inside the egg.
- kazinator 3y agoAlso, why do we say "four legged table" in reference to common, rectangular tables? The position of the fourth leg is determined from the other three, so it shouldn't count!
- rantallion 3y ago
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- etwigg 3y agoI didn't know an egg could be so beautiful <3
- 1970-01-01 3y agoEggcellent :)
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- quickthrower2 3y ago()
- bongripper 3y ago[dead]
- ks2048 3y agoNice. I wonder how closely it could be approximated with a small number of Bezier curves. (for example, a quadratic with six points. 4 control points and two side points).
- ryandrake 3y agoI wonder if you could make it even more "beautiful" by gradually easing between the various curvatures rather than having the discontinuities at the intersections of the curves. Kind of like the difference between a square with rounded corners and a "squircle"[1]. 1: https://webflow.com/blog/squircle-vs-rounded-squares https://webflow.com/blog/squircle-vs-rounded-squares
- alexchamberlain 3y agoDo you have discontinuities though? The tangents at the point of intersection match.
- fanf2 3y agoThere is a discontinuity in curvature where each arc meets. It’s possible to make joins between curves smoother using Euler spirals, but I don’t know how to use them well enough to apply them to eggs. https://en.m.wikipedia.org/wiki/Euler_spiral https://en.m.wikipedia.org/wiki/Euler_spiral I recently tried to draw f holes using Euler spirals, but they turned out too short and fat, and I gave up on them. But they are quite fun to draw on a computer by simple numerical integration, ignoring all the more complicated mathematics in the wikipedia article. Perhaps I could have made my f holes more elegant by understanding the parts I ignored… https://en.m.wikipedia.org/wiki/Sound_hole https://en.m.wikipedia.org/wiki/Sound_hole
- notfish 3y agoI do hate when f holes are too short and fat, but yes: understanding the parts you generally ignore might help.
- pimlottc 3y agoThe issue is more the smoothness in the change in curvy-ness: https://www.figma.com/blog/desperately-seeking-squircles/ https://www.figma.com/blog/desperately-seeking-squircles/
- onetimeuse92304 3y ago
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- blt 3y agoHere's a more analytical approach to constructing egg geometry: https://kar.kent.ac.uk/89885/ https://kar.kent.ac.uk/89885/
- twic 3y agoAnd a purely empirical approach: https://www.imperial.ac.uk/news/179909/how-birds-determines-shape-their-eggs/ https://www.imperial.ac.uk/news/179909/how-birds-determines-...
- throwaway2037 3y agoWho is the "Moss" in Moss's egg? I assume it is a person, but I cannot find anything when I search.
- jhardy54 3y agoThis led me on a bit of a rabbit hole, but I’m suspicious that Moss may refer to Stephanie Moss, who is referenced in the preface of Mathographic by Robert Dixon.