A gnomonic map projection is a map projection which displays all great circles as straight lines, resulting in any straight line segment on a gnomonic map showing a geodesic, the shortest route between the segment's two endpoints. This is achieved by casting surface points of the sphere onto a tangent plane, each landing where a ray from the center of the sphere passes through the point on the surface and then on to the plane. No distortion occurs at the tangent point, but distortion increases rapidly away from it. Less than half of the sphere can be projected onto a finite map. Consequently, a rectilinear photographic lens, which is based on the gnomonic principle, cannot image more than 180 degrees. (Wikipedia).
Parametrizing and projecting a sphere | Universal Hyperbolic Geometry 38 | NJ Wildberger
This video introduces stereographic and gnomonic projections of a sphere. We begin by reviewing three dimensional coordinate systems. A rational parametrization of a sphere is analogous to the rational parametrization of a circle found in MathFoundations29. Stereographic projection project
From playlist Universal Hyperbolic Geometry
Projection of One Vector onto Another Vector
Link: https://www.geogebra.org/m/wjG2RjjZ
From playlist Trigonometry: Dynamic Interactives!
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
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
This video explains how to determine the projection of one vector onto another vector. http://mathispower4u.yolasite.com/
From playlist Vectors
Ex: Vector Projection in Three Dimensions
This video explains how to determine the projection of one vector onto another vector in three dimensions. Site: http://mathispower4u.com
From playlist Vectors in Space (3D)
Follow Michael Stevens: http://www.twitter.com/tweetsauce EXTRA INFO & LINKS BELOW! Dr. Julian Bayliss' rainforest story: http://youtu.be/mni8mSS4KDU Cool video from CGPGrey: "How Many Countries Are There?" http://youtu.be/4AivEQmfPpk upside-down map: http://paulmencke.nl.dualdev.com/wp
From playlist DOT.
Squeaks broke his watch! Luckily Jessi knows of a handy way to tell time, with a sundial! Hi there! We at SciShow want to learn more about you and your opinions! If you have time, please take a moment to fill out this survey: https://www.surveymonkey.com/r/SciShowSurvey2017 Thank you! --
From playlist SciShow Kids
Algebra of the Sun - Russell Goyder
Russell Goyder presents an approach to the "sundial problem" of computing the length of a shadow cast by a stick (gnomon) by the sun at a given latitude at a given time of day, at a given point of the Earth's orbit, using geometric algebra. The webpage for this seminar is https://metauni.
From playlist Anything At All seminar
If Corresponding Angles are Congruent, then...?
Link: https://www.geogebra.org/m/hb3xXZeF
From playlist Geometry: Dynamic Interactives!
This is a short, animated visual proof demonstrating the sum of the infinite geometric series with ratio -1/2. For a longer version of this animation (with dramatic music only), check out : https://youtu.be/wLPsEULfPnk This animation is based on a visual proof by Roger B. Nelsen from th
From playlist MathShorts
Getting Started with GeoGebra Augmented Reality
Here's a quick screencast that illustrates how you can use GeoGebra Augmented Reality to model every-day, real-life, 3D objects. In addition, we'll take a virtual exploration of the 4 main conic section types (circle, parabola, ellipse, hyperbola).
From playlist GeoGebra Augmented Reality Demos (Older iOS App)
Quaternions as 4x4 Matrices - Connections to Linear Algebra
In math, it's usually possible to view an object or concept from many different (but equivalent) angles. In this video, we will see that the quaternions may be viewed as 4x4 real-valued matrices of a special form. What is interesting here is that if you know how to multiply matrices, you a
From playlist Quaternions
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
Sum of odd integers: a generalization (visual proof)
This short animated proof demonstrates the classic sum of odds visual proof and then shows one way to extend the idea to finding sums in other polygonal arrays. Surprisingly, the natural extension to finding sums of certain entries in a triangular array yields the sequence of squares. We l
From playlist Finite Sums
To learn more about Wolfram Technology Conference, please visit: https://www.wolfram.com/events/technology-conference/ Speaker: Paritosh Mokhasi Wolfram developers and colleagues discussed the latest in innovative technologies for cloud computing, interactive deployment, mobile devices,
From playlist Wolfram Technology Conference 2017
From Sundials to Crystals: A Brief History of Timekeeping
How did early humans keep time, and what exactly is a "leap second?" Join Michael Aranda on SciShow as we dive into the long and strange history of timekeeping. Let's go! ---------- Dooblydoo thanks go to the following Patreon supporters -- we couldn't make SciShow without them! Shout out
From playlist SciShow Infusion
Adding Vectors Geometrically: Dynamic Illustration
Link: https://www.geogebra.org/m/tsBer5An
From playlist Trigonometry: Dynamic Interactives!
Non-Euclidean Geometry Explained - Hyperbolica Devlog #1
I present the easiest way to understand curved spaces, in both hyperbolic and spherical geometries. This is the first in a series about the development of Hyperbolica. Chapters: 0:00 Intro 0:24 Spherical Geometry 2:33 Hyperbolic Introduction 3:53 Projections 5:37 Non-Euclidean Weirdness
From playlist Fractals & Math