Uploaded June 2017 | Updated September 2026, 1 week ago
demonstrations.wolfram.com/FiveConcyclicPointsInATriangle
The Wolfram Demonstrations Project contains thousands of free interactive visualizations, with new entries added daily.
Let ABC be a triangle with incenter I. Let A_1, B_1, C_1 be the projections of I on the sides of ABC. Let F be the intersection of the lines AI and A_1C_1. Then A_1, C, B_1, I and F lie on the dashed black circle of diameter CI, and the lines AI and CF ...
Contributed by: Jean Michel Tardieux
Audio created with WolframTones:
tones.wolfram.com
demonstrations.wolfram.com/FiveConcyclicPointsInATriangle
The Wolfram Demonstrations Project contains thousands of free interactive visualizations, with new entries added daily.
Let ABC be a triangle with incenter I. Let A_1, B_1, C_1 be the projections of I on the sides of ABC. Let F be the intersection of the lines AI and A_1C_1. Then A_1, C, B_1, I and F lie on the dashed black circle of diameter CI, and the lines AI and CF ...
Contributed by: Jean Michel Tardieux
Audio created with WolframTones:
tones.wolfram.com

![Roulette (Epitrochogon) of a Regular Polygon Rolling around Another Regular Polygon
http://demonstrations.wolfram.com/RouletteEpitrochogonOfARegularPolygonRollingAroundAnotherReg
The Wolfram Demonstrations Project contains thousands of free interactive visualizations, with new entries added daily.
An epitrochogon is the trace (roulette) of a point attached to a polygon rolling without slipping around the outside of another polygon [1]. The epitrochogon can be curtate if the tracing point is inside the rolling polygon, or prolate if it is outside....
Contributed by: Erik Mahieu
Audio created with WolframTones:
http://tones.wolfram.com Roulette (Epitrochogon) of a Regular Polygon Rolling around Another Regular Polygon](https://i.ytimg.com/vi/PRnFjPaAGYI/mqdefault.jpg)

![First[{}]
http://demonstrations.wolfram.com/ThePlemeljConstructionOfATriangle10
The Wolfram Demonstrations Project contains thousands of free interactive visualizations, with new entries added daily.
First[{}]
First[{}]
Audio created with WolframTones:
http://tones.wolfram.com First[{}]](https://i.ytimg.com/vi/Q92cVJQ5UAc/mqdefault.jpg)


![Linear Regression with Gradient Descent
http://demonstrations.wolfram.com/LinearRegressionWithGradientDescent
The Wolfram Demonstrations Project contains thousands of free interactive visualizations, with new entries added daily.
This Demonstration shows how linear regression can determine the best fit to a collection of points by iteratively applying gradient descent. Linear regression works by minimizing the error function: ( 1 ) / ( n ) UnderoverscriptBox[?, RowBox[{i, =, 1}]...
Contributed by: Jonathan Kogan
Audio created with WolframTones:
http://tones.wolfram.com Linear Regression with Gradient Descent](https://i.ytimg.com/vi/QmlOzt7GleI/mqdefault.jpg)


![Comparing the Cook-Torrance BRDF Model with Diffuse Reflection Simulation
http://demonstrations.wolfram.com/ComparingTheCookTorranceBRDFModelWithDiffuseReflectionSimula
The Wolfram Demonstrations Project contains thousands of free interactive visualizations, with new entries added daily.
As Wolfgang Pauli said, [OpenCurlyDoubleQuote]God made the bulk; the surface was invented by the devil.[CloseCurlyDoubleQuote] This Demonstration illustrates the diabolical characteristics of surfaces in the case of reflection. In this specific case, ...
Contributed by: D. Meliga, S. Z. Lavagnino and G. Valorio
Audio created with WolframTones:
http://tones.wolfram.com Comparing the Cook-Torrance BRDF Model with Diffuse Reflection Simulation](https://i.ytimg.com/vi/RY4wIrQ8Gqc/mqdefault.jpg)
