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Algebraic Curves, MATHEMATICA® Animations
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This page exhibits 10 MATHEMATICA® Animations of algebraic curves with nodes and cusp points. A notebook with the animations and source code is available.

Subject:
Mathematics
Algebra
Material Type:
Interactive
Provider:
California State University
Provider Set:
National Curve Bank
Author:
Gray, Shirley
Maeva, Oksana
Area of a Surface of Revolution
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This page discusses calculating areas of surfaces of revolution with animations, formulas, and examples. Special attention is paid to the paradox illustrated by Gabriel's horn or Torricelli's Trumpet.

Subject:
Mathematics
Material Type:
Interactive
Provider:
California State University
Provider Set:
National Curve Bank
Author:
Gray, Shirley
Talman, Lou
Astroid
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The page discusses the curve known as an astroid or hypocycloid of four cusps. In one quadrant, the astroid may be thought of as a falling ladder,a problem often found inintroductory Calculus. In thiscase, the curve is also known as a glissette.

Subject:
Mathematics
Material Type:
Interactive
Provider:
California State University
Provider Set:
National Curve Bank
Author:
Gray, Shirley
The Brachistochrone
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This page contains a discussion of the Brachistochrone problem and an animation showing a particle sliding down a line and a cycloid.There are links to 4 additional pageswith different approaches to the Brachistochrone problem. Interesting historical notes.

Subject:
Mathematics
Material Type:
Interactive
Provider:
California State University
Provider Set:
National Curve Bank
Author:
Gray, Shirley
Qawasmi, Abel
A Collection of Famous Plane Curves created in POVRAY
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This page contains 3-dimensional surfaces ploted in color using POVRAY (Persistence Of Vision RAY tracing). There are links to pages containg the code for the plots and to a page of references and additonal plots.

Subject:
Mathematics
Material Type:
Diagram/Illustration
Provider:
California State University
Provider Set:
National Curve Bank
Author:
Gleason, Patrick J.
Gray, Shirley
The Conics and Stereographic Projection
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A power Point slide show is used for this animation. Points on the plane are associated with points on a sphere by stereographic projection. The north pole of the sphere corresponds to the point at infinity. This is the one point compactification of the plane.

Subject:
Mathematics
Material Type:
Interactive
Provider:
California State University
Provider Set:
National Curve Bank
Author:
Gray, Shirley
Groah, Jeffery M.
The Curve of Clavería
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A page which celebrates the 2008 International Exposition Zaragoza. The properties of the Oblique Cone and the Curve of Claveria are explained. The text is in Spanish.

Subject:
Law
General Law
Mathematics
Material Type:
Interactive
Provider:
California State University
Provider Set:
National Curve Bank
Author:
Gray, Shirley
Vila, Pedro L. Claveria
Curves of Constant Width and Reuleaux Polygons
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This page features information on constant width curves, also known as Orbiform Curves or Reuleaux Polygons. One application is to the Wankel Engine. The page contains animations, plots, an historical sketch, and links to Mathematica code.

Subject:
Mathematics
Material Type:
Interactive
Provider:
California State University
Provider Set:
National Curve Bank
Author:
Gray, Shirley
Derivation of the Formula for the Area of a Circle
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Animations of the area formula for the circle and a proof of the Pythagorean Theorem. Based on The Nine Chapters on the Mathematical Art, by Liu Hui (ca. 250 AD). . . .

Subject:
Mathematics
Material Type:
Interactive
Provider:
California State University
Provider Set:
National Curve Bank
Author:
Gray, Shirley
Richmond, Bettina
Richmond, Tom
Exploring Area between Curves
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Calculus texts have problems on finding the Areas between Curves in the chapters on applications of Integration. The NCB suggests finding some of these examples in a text and trying them in Harumi's graph. Experimenting on a computer with the approximation for finding the area using rectangles is fascinating. As the number of rectangles increases, the approximation improves. Therefore, mathematicians define the area A between the two curves as the limit of the sum of the areas of these approximating rectangles where n is the number of rectangles bounded between a and b.

Subject:
Mathematics
Material Type:
Interactive
Provider:
California State University
Provider Set:
National Curve Bank
Author:
Gray, Shirley
Monroy, Harumi