This page exhibits 10 MATHEMATICA® Animations of algebraic curves with nodes and cusp points. A notebook with the animations and source code is available.
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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.
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.
This page features a mathematical art project consisting of a Generation 3 Sierpinski tetrahedron made from 384 baseball bats and 130 baseballs.
A Power Point Slide Show which features the life and work of Rafael Bombelli, 1526-1572. In particular his work with negative and imaginary numbers.
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.
A discussion of quilts created to represent the Cayley table for the quaternion group and for the intersection of this group with D4.
This is a page devoted to the cissoid of Diocles with equations, animations, and history of its relation to the duplication of the cube problem.
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.
A comparison of time of travel between different variational methods and the minimizing cycloid. Brachistochrone Cycloid
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.
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.
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.
Definitions, explanations, and Maple code for animations of the cycloid, trochoid, epicycloid, hypocycloid, epitrochoid, and hypotrochoid
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). . . .
This page contains a discussion of Euler paths and Euler circuits with animated illustrations. Euler was motivated by the Koenigsberg Bridge Problem.
Animations generate the Evolute of the Semi-Cubical Parabola. Interesting side notes and links for William Neile and Cardan.
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.
This page is devoted to Rene Descartes and his equiangular spiral. It contains an historical sketch, equations, and graphics including pictures of Descartes postage stamps.
The NCB suggests trying examples from your homework in Harumi's interactive graph. This is often helpful. Rational functions with vertical, horizontal and slant asymptotes are especially fun.