John Oprea: New Applications
http://www.maplesoft.com/applications/author.aspx?mid=154
en-us2017 Maplesoft, A Division of Waterloo Maple Inc.Maplesoft Document SystemSun, 28 May 2017 22:06:17 GMTSun, 28 May 2017 22:06:17 GMTNew applications published by John Opreahttp://www.mapleprimes.com/images/mapleapps.gifJohn Oprea: New Applications
http://www.maplesoft.com/applications/author.aspx?mid=154
Mandelbrot set
http://www.maplesoft.com/applications/view.aspx?SID=3503&ref=Feed
Shows how to generate a graphic of the Mandelbrot set using Maple plots<img src="/view.aspx?si=3503/mandelbrot.gif" alt="Mandelbrot set" align="left"/>Shows how to generate a graphic of the Mandelbrot set using Maple plots3503Mon, 18 Jun 2001 00:00:00 ZJohn OpreaJohn OpreaGeodesic on a Cone
http://www.maplesoft.com/applications/view.aspx?SID=3575&ref=Feed
This worksheet shows how to draw geodesics on the cone as well as how to calculate the arclength of a geodesic. <img src="/view.aspx?si=3575//applications/images/app_image_blank_lg.jpg" alt="Geodesic on a Cone" align="left"/>This worksheet shows how to draw geodesics on the cone as well as how to calculate the arclength of a geodesic. 3575Mon, 18 Jun 2001 00:00:00 ZJohn OpreaJohn OpreaDetermining a parametrized curve from its curvature and torsion
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This worksheet contains some basic applications of MAPLE to the differential geometry of curves. In particular, there are procedures for computing the curvature and torsion of curves, and for determining a curve solely from its curvature and/or torsion.
<img src="/view.aspx?si=3576//applications/images/app_image_blank_lg.jpg" alt="Determining a parametrized curve from its curvature and torsion" align="left"/>This worksheet contains some basic applications of MAPLE to the differential geometry of curves. In particular, there are procedures for computing the curvature and torsion of curves, and for determining a curve solely from its curvature and/or torsion.
3576Mon, 18 Jun 2001 00:00:00 ZJohn OpreaJohn OpreaEvolutes and involutes of curves in the plane, with applications to 18th century sea navigation
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This worksheet deals with special types of curves called involutes and evolutes. These are curves which can be associated to any given curve alpha. An involute to alpha may be thought of as any curve which is always perpendicular to the tangent lines of alpha . If you think of unwinding string tautly from around a curve, you will get a picture of an involute. An evolute of is a curve whose involute is alpha, so evolutes and involutes are, in a sense, inverses to each other. An evolute of may also be thought of as the curve determined by the centers of curvature of alpha. Involutes are used in gear tooth design to eliminate vibration as much as possible, while the involute and evolute of a very special curve can be used to design a special type of clock.<img src="/view.aspx?si=3577//applications/images/app_image_blank_lg.jpg" alt="Evolutes and involutes of curves in the plane, with applications to 18th century sea navigation" align="left"/>This worksheet deals with special types of curves called involutes and evolutes. These are curves which can be associated to any given curve alpha. An involute to alpha may be thought of as any curve which is always perpendicular to the tangent lines of alpha . If you think of unwinding string tautly from around a curve, you will get a picture of an involute. An evolute of is a curve whose involute is alpha, so evolutes and involutes are, in a sense, inverses to each other. An evolute of may also be thought of as the curve determined by the centers of curvature of alpha. Involutes are used in gear tooth design to eliminate vibration as much as possible, while the involute and evolute of a very special curve can be used to design a special type of clock.3577Mon, 18 Jun 2001 00:00:00 ZJohn OpreaJohn OpreaFlat surfaces of revolution
http://www.maplesoft.com/applications/view.aspx?SID=3578&ref=Feed
This worksheet shows how Maple may be used to find flat surfaces of revolution. Recall that a surface is flat if its Gauss curvature vanishes.<img src="/view.aspx?si=3578//applications/images/app_image_blank_lg.jpg" alt="Flat surfaces of revolution" align="left"/>This worksheet shows how Maple may be used to find flat surfaces of revolution. Recall that a surface is flat if its Gauss curvature vanishes.3578Mon, 18 Jun 2001 00:00:00 ZJohn OpreaJohn OpreaGaussian and mean curvature
http://www.maplesoft.com/applications/view.aspx?SID=3579&ref=Feed
This worksheet contains basic procedures for computing Gauss curvature and mean curvature. Also, several important surfaces and examples of their plots are given.<img src="/view.aspx?si=3579//applications/images/app_image_blank_lg.jpg" alt="Gaussian and mean curvature" align="left"/>This worksheet contains basic procedures for computing Gauss curvature and mean curvature. Also, several important surfaces and examples of their plots are given.3579Mon, 18 Jun 2001 00:00:00 ZJohn OpreaJohn OpreaIntroduction to the mathematics of maps
http://www.maplesoft.com/applications/view.aspx?SID=3581&ref=Feed
There are hundreds of map projections that have been described in the cartographic literature. It is our objective here to describe Maple tools that can be used in their creation<img src="/view.aspx?si=3581//applications/images/app_image_blank_lg.jpg" alt="Introduction to the mathematics of maps" align="left"/>There are hundreds of map projections that have been described in the cartographic literature. It is our objective here to describe Maple tools that can be used in their creation3581Mon, 18 Jun 2001 00:00:00 ZRichard BaurRichard BaurCylindrical projections
http://www.maplesoft.com/applications/view.aspx?SID=3582&ref=Feed
Maple displays the Mercator projection of the earth which is probably the best known of all projections<img src="/view.aspx?si=3582//applications/images/app_image_blank_lg.jpg" alt="Cylindrical projections" align="left"/>Maple displays the Mercator projection of the earth which is probably the best known of all projections3582Mon, 18 Jun 2001 00:00:00 ZRichard BaurRichard BaurAzimuthal projections
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Five azimuthal projections are discussed in this application including equal area, gnomonic, equidistant, stereographic, and orthographic.
<img src="/view.aspx?si=3583//applications/images/app_image_blank_lg.jpg" alt="Azimuthal projections" align="left"/>Five azimuthal projections are discussed in this application including equal area, gnomonic, equidistant, stereographic, and orthographic.
3583Mon, 18 Jun 2001 00:00:00 ZRichard BaurRichard BaurPseudocylindrical projections
http://www.maplesoft.com/applications/view.aspx?SID=3584&ref=Feed
The Mollweide Projection is an equal area pseudocylindrical with meridians as semi-ellipses. This projection of the earth is displayed here.<img src="/view.aspx?si=3584//applications/images/app_image_blank_lg.jpg" alt="Pseudocylindrical projections" align="left"/>The Mollweide Projection is an equal area pseudocylindrical with meridians as semi-ellipses. This projection of the earth is displayed here.3584Mon, 18 Jun 2001 00:00:00 ZRichard BaurRichard BaurProjections of the National Geographic Society
http://www.maplesoft.com/applications/view.aspx?SID=3585&ref=Feed
The Winkel Tripel projection of the world was adopted by the National Geographic Society and the Times Atlas is displayed in this application.<img src="/view.aspx?si=3585//applications/images/app_image_blank_lg.jpg" alt="Projections of the National Geographic Society" align="left"/>The Winkel Tripel projection of the world was adopted by the National Geographic Society and the Times Atlas is displayed in this application.3585Mon, 18 Jun 2001 00:00:00 ZRichard BaurRichard BaurTransverse projections
http://www.maplesoft.com/applications/view.aspx?SID=3586&ref=Feed
The Cassini Projection of the earth is defined and presented here.<img src="/view.aspx?si=3586//applications/images/app_image_blank_lg.jpg" alt="Transverse projections" align="left"/>The Cassini Projection of the earth is defined and presented here.3586Mon, 18 Jun 2001 00:00:00 ZRichard BaurRichard BaurHybrid projections
http://www.maplesoft.com/applications/view.aspx?SID=3587&ref=Feed
Hybrid projections called sinusoidal and Mollweide projections are used to display the earth using Maple <img src="/view.aspx?si=3587//applications/images/app_image_blank_lg.jpg" alt="Hybrid projections" align="left"/>Hybrid projections called sinusoidal and Mollweide projections are used to display the earth using Maple 3587Mon, 18 Jun 2001 00:00:00 ZRichard BaurRichard BaurInterrupted projections
http://www.maplesoft.com/applications/view.aspx?SID=3588&ref=Feed
Interrupted projections are those in which the northern and/or southern hemispheres are divided into a number of lobes. Interrupted Mollweide and Interrupted Homolosine are defined and displayed in this application<img src="/view.aspx?si=3588//applications/images/app_image_blank_lg.jpg" alt="Interrupted projections" align="left"/>Interrupted projections are those in which the northern and/or southern hemispheres are divided into a number of lobes. Interrupted Mollweide and Interrupted Homolosine are defined and displayed in this application3588Mon, 18 Jun 2001 00:00:00 ZRichard BaurRichard BaurMore miscellaneous projections
http://www.maplesoft.com/applications/view.aspx?SID=3590&ref=Feed
More miscellaneous projections of the world are presented here which include Wiechel "Catherine Wheel" projection, Collignon Triangle projection, "Lagrange" Projection and Briesemeister Projection. <img src="/view.aspx?si=3590//applications/images/app_image_blank_lg.jpg" alt="More miscellaneous projections" align="left"/>More miscellaneous projections of the world are presented here which include Wiechel "Catherine Wheel" projection, Collignon Triangle projection, "Lagrange" Projection and Briesemeister Projection. 3590Mon, 18 Jun 2001 00:00:00 ZRichard BaurRichard BaurMap distortion
http://www.maplesoft.com/applications/view.aspx?SID=3591&ref=Feed
This application describes the extent to which different projections distort the original pattern of the surface of the earth when developing map projections.
<img src="/view.aspx?si=3591//applications/images/app_image_blank_lg.jpg" alt="Map distortion" align="left"/>This application describes the extent to which different projections distort the original pattern of the surface of the earth when developing map projections.
3591Mon, 18 Jun 2001 00:00:00 ZRichard BaurRichard BaurMathematics of map projections
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A simple procedure to calculate the metric coefficients of a surface parametrized by theta and phi (since we will be dealing with the sphere) is presented here. A small bit of area on a surface is approximated by the parallelogram spanned by tangent vectors. Finally, a procedure is included to calculate the Gauss curvature of a surface directly from metric coefficients<img src="/view.aspx?si=3592//applications/images/app_image_blank_lg.jpg" alt="Mathematics of map projections" align="left"/>A simple procedure to calculate the metric coefficients of a surface parametrized by theta and phi (since we will be dealing with the sphere) is presented here. A small bit of area on a surface is approximated by the parallelogram spanned by tangent vectors. Finally, a procedure is included to calculate the Gauss curvature of a surface directly from metric coefficients3592Mon, 18 Jun 2001 00:00:00 ZRichard BaurRichard BaurMiscellaneous projections - Peirce Quincuncial
http://www.maplesoft.com/applications/view.aspx?SID=3589&ref=Feed
The Peirce Quincuncial projection of the world is presented in this application.<img src="/applications/images/app_image_blank_lg.jpg" alt="Miscellaneous projections - Peirce Quincuncial" align="left"/>The Peirce Quincuncial projection of the world is presented in this application.3589Sun, 17 Jun 2001 04:00:00 ZRichard BaurRichard Baur