Conformal mappings | Projective geometry
In mathematics, a stereographic projection is a perspective projection of the sphere, through a specific point on the sphere (the pole or center of projection), onto a plane (the projection plane) perpendicular to the diameter through the point. It is a smooth, bijective function from the entire sphere except the center of projection to the entire plane. It maps circles on the sphere to circles or lines on the plane, and is conformal, meaning that it preserves angles at which curves meet and thus locally approximately preserves shapes. It is neither isometric (distance preserving) nor equiareal (area preserving). The stereographic projection gives a way to represent a sphere by a plane. The metric induced by the inverse stereographic projection from the plane to the sphere defines a geodesic distance between points in the plane equal to the spherical distance between the spherical points they represent. A two-dimensional coordinate system on the stereographic plane is an alternative setting for spherical analytic geometry instead of spherical polar coordinates or three-dimensional cartesian coordinates. This is the spherical analog of the Poincaré disk model of the hyperbolic plane. Intuitively, the stereographic projection is a way of picturing the sphere as the plane, with some inevitable compromises. Because the sphere and the plane appear in many areas of mathematics and its applications, so does the stereographic projection; it finds use in diverse fields including complex analysis, cartography, geology, and photography. Sometimes stereographic computations are done graphically using a special kind of graph paper called a stereographic net, shortened to stereonet, or Wulff net. (Wikipedia).
This shows a 3d print of a mathematical sculpture I produced using shapeways.com. This model is available at http://shpws.me/q41V.
From playlist 3D printing
Further adventures in stereographic projection
These stereographic projection models are available from my Shapeways shop: https://www.shapeways.com/shops/henryseg?section=Stereographic+Projection The torch/flashlight is a Mini Maglite AAA LED flashlight (http://maglite.com/shop/mini-maglite-led-2-cell-aaa-flashlight.html).
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I originally took this photo illustrating stereographic projection in 2014. Soon after, someone attached a click-bait caption to the image, and it has been bouncing around the internet ever since. Here, I explain what the image is really about. You can buy these stereographic projection
From playlist 3D printing
LIGHT shadow (stereographic projection)
Stereographic projection spheres available at https://www.shapeways.com/shops/henryseg?section=Stereographic+Projection
From playlist 3D printing
"Seeing in 3D" discusses the basics of stereoscopic human vision, examines the most common types of S3D displays available today, and even asserts a humorous look into the future.
From playlist IU Pervasive Technology Institute and the TeraGrid
Stereolab "Ticker Tape Of The Unconscious" (Montage)
Taken from the album "Dots And Loops".
From playlist the absolute best of stereolab
Sometimes a closeup works best, but other times you may want a wider-angle shot. You can experiment by moving closer and farther away from your subject, or by using your camera's zoom. We hope you enjoy! To learn more, check out our written lesson here: https://edu.gcfglobal.org/en/digita
From playlist Digital Photography
If you are interested in learning more about this topic, please visit http://www.gcflearnfree.org/ to view the entire tutorial on our website. It includes instructional text, informational graphics, examples, and even interactives for you to practice and apply what you've learned.
From playlist 3D Printing
Most Insane Immersive Movie Experience EVER, Part 1
Check out this guy's room totally change into the movie he is watching! No SFX, no post production, no cuts, everything you see here is 100% for real. We were funded by the Video Store of PlayStation® Store (http://www.greatfilmsfillrooms.com) to make a series of movie related videos us
From playlist Projection Mapping inspirations
Turning Spheres Into Squares—Stereographic Projection
In this video I show you how stereographic projection works and how you can map spheres onto 2d planes and even make some really neat photographs! Get Your Experiment Box Here: https://theactionlab.com/ Checkout my experiment book: https://amzn.to/2Wf07x1 Follow me on Twitter: https://tw
From playlist Amazing 3D Printed Objects
Illuminating hyperbolic geometry
Joint work with Saul Schleimer. In this short video we show how various models of hyperbolic geometry can be obtained from the hemisphere model via stereographic and orthogonal projection. 2D figure credits: 4:09 Cannon, Floyd, Kenyon, Parry. 0:49, 1:20, 1:31, 2:12, Roice Nelson. We th
From playlist 3D printing
"Illustrating Geometry" exhibition at SCGP, Artist's talk: "Sculpture in four-dimensions"
Slides: http://www.math.okstate.edu/~segerman/talks/sculpture_in_4-dimensions.pdf This video is also available at the Simons Center website, at http://scgp.stonybrook.edu/archives/11540 Thanks to Josh Klein for filming and editing.
From playlist 3D printing
Laboratórios Virtuais de Cálculo, Álgebra e Geometria
Práticas de ensino de matemática na engenharia com a tecnologia Wolfram pelo Dr. Márcio Antonio de Faria Rosa DA Universidade Estadual de Campinas (UNICAMP)
From playlist Conferência Brasileira Virtual de tecnologia Wolfram
Steiner's Porism: proving a cool animation #SoME1
Strange circle stuff. (Some people have commented that the audio is really low. Unfortunately I haven't found a way to fix it without re-uploading the whole video, but your feedback will be taken on board for the next video! Also to everyone begging for more content, I’m currently in the m
From playlist Summer of Math Exposition Youtube Videos
This lecture continues our discussion of the sphere, relating inversive geometry on the plane to the more fundamental inversive geometry of the sphere, introducing the Riemann sphere model of the complex plane with a point at infinity. Then we discuss the sphere as the projective line ove
From playlist Algebraic Topology: a beginner's course - N J Wildberger
reaLD 3D glasses filter with a linear polarising filter
This is for a post on my blog: http://blog.stevemould.com
From playlist Everything in chronological order
2014 Hari Shankar Memorial lecture: "How to make sculptures of 4-dimensional things"
The Hari Shankar Memorial Lecture is an annual public lecture held at the University of Northern Iowa. Slides: https://www.math.okstate.edu/~segerman/talks/how_to_make_sculptures_of_4d_things.pdf
From playlist 3D printing