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A Geometric Construction of the Parabola

► A Matthen's creation>>
http://blog.matthen.com/post/6000287357/a-geometric-construction-of-the-parabola-the-blue

The blue point is called the focus, and the horizontal line is the directrix. The blue lines show all the points which are at an equal distance from the red point and the blue focus point.
The point of the blue line directly above the red dot contributes to the parabolic curve, because the parabola is defined as the set of all points equidistant to the focus and the directrix.

► Go to the code>> https://pastebin.com/k5FrFVfp

Further reading

► Constructing a Parabola>> http://jwilson.coe.uga.edu/EMAT6680Fa07/O%27Kelley/Assignment%206/Parabola.html

► Methods of constructing parabolas>> http://www3.ul.ie/~rynnet/swconics/SP.htm

#Mathematics, #GeometricCurves, #Geometry, #ConicSections, #Animations

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* A visual proof that ¼ + 1/16 + 1/64 + … = 1/3*

Work by +Matthew Henderson
http://blog.matthen.com/

#math #animation #science #coding

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Anything Goes

A creation from Clayton Shonkwiler, mathematician and artist.

He wrote:

"It's an obvious but kind of cool fact that every quadrilateral tiles the plane. Building on some ideas from Cut the Knot, I decided to write a function which would, given the edges of a quadrilateral (as vectors), produce a tessellation. Here's what I ended up with."

► Go to the source, where you can get the code>> http://community.wolfram.com/groups/-/m/t/865171

Further reading

► Simple Quadrilaterals Tessellate the Plane>>
http://www.cut-the-knot.org/Curriculum/Geometry/QuadTessellation.shtml


#Mathematics, #Art, #Tesselation, #QuadrilateralTiles, #Geometry

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"The pyramid shape is said to hold many secrets and amazing properties. One of them is a sense of wonder.” 
― Vera Nazarian

Work by Charlie Deck

#C4D #animation #math

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Osculating Circles to a Polar Curve

A nice creation by Clayton Shonkwiler.

This animation shows 100 osculating circles to the curve r = cos(3 θ + π /2) as they traverse along the curve.

► Go to this link for more information and for the code: http://community.wolfram.com/groups/-/m/t/1114049

Clayton Shonkwiler is a mathematician and artist at Colorado State University.

About him, by his own words:
"I am interested in geometric models of physical systems; currently I'm mostly focused on geometric approaches to studying random walks with topological constraints, which are used to model polymers.

My art is often inspired by the mathematics that arise in my research and teaching, but more generally I enjoy turning interesting and non-trivial mathematics into art."

► Visit his website: https://shonkwiler.org/


#Mathematics, #Art, #Geometry, #OsculatingCircles, #Animation

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Cos Roll
Rolling a circle in a circle to draw a cosine wave

Work by +Matthew Henderson
Code: https://pastebin.com/w1GuX3XC

#math #science #cosine #coding

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Resonance clock
“Life is a full circle, widening until it joins the circle motions of the infinite.”
~ Anaïs Nin

Work by +bigblueboo

#math #processing #animation

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#CirclesCounted: 84

Bees & Bombs is letting us count again ;)
https://beesandbombs.tumblr.com/post/163256181074/hue-strip

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Sum of Interior Angles of a Triangle

A simple and captivating visualization that helps us to understand dynamically the triangle postulate, in Euclidean geometry.

► Source>> http://www.mathwarehouse.com

#Mathematics, #EuclideanGeometry, #EducationalAnimations

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Disc Expansion

Charlie Deck's work

#math #coding #processing #animation
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