MaplePrimes - comments on Blog Entry, It's Better With Maple

MaplePrimes - comments on Blog Entry, It's Better With Maple http://www.mapleprimes.com/maplesoftblog/35171-Its-Better-With-Maple en-us 2026 Maplesoft, A Division of Waterloo Maple Inc. Maplesoft Document System Tue, 09 Jun 2026 14:16:01 GMT Tue, 09 Jun 2026 14:16:01 GMT The latest comments added to the Blog Entry, It's Better With Maple http://www.mapleprimes.com/images/mapleprimeswhite.jpg MaplePrimes - comments on Blog Entry, It's Better With Maple http://www.mapleprimes.com/maplesoftblog/35171-Its-Better-With-Maple Here's code for two different ways to animate the graph with(plots): animate(p... http://www.mapleprimes.com/maplesoftblog/35171-Its-Better-With-Maple?ref=Feed:MaplePrimes:It's Better With Maple:Comments#comment35174 Here's code for two different ways to animate the graph with(plots): animate(plot,[x2+t,x=-2..2],t=0..1); and the second way with(plots): display(seq(plot(x2+t/20,x=-2..2),t=0..20),insequence=true);     The latest comments added to the Blog Entry, It's Better With Maple 35174 Sat, 13 Feb 2010 18:37:05 Z Christopher Christopher As a physicist in a math department, I think being able to write an equatio... http://www.mapleprimes.com/maplesoftblog/35171-Its-Better-With-Maple?ref=Feed:MaplePrimes:It's Better With Maple:Comments#comment35275 As a physicist in a math department, I think being able to write an equation for the tangent line at an arbitrary point on a curve, and then place a condition on it to solve some interesting problem, is a perfect example of what calculus is all about, and of course Maple is the perfect tool to do this. Your example here is really inspiring. But I am only one person in a big department very aware that my colleagues and even our textbook whose author built a 24 million dollar house from his profits will not support me in being different from the norm, so I have wimped out. The latest comments added to the Blog Entry, It's Better With Maple 35275 Fri, 19 Mar 2010 19:32:56 Z Dr. Robert Jantzen Dr. Robert Jantzen I cannot resist adding another comment. If you had animated this graph but going... http://www.mapleprimes.com/maplesoftblog/35171-Its-Better-With-Maple?ref=Feed:MaplePrimes:It's Better With Maple:Comments#comment35276 I cannot resist adding another comment. If you had animated this graph but going inside the original parabola instead of outside, you would have seen the normals forming a caustic curve: the evolute of the parabola. I have a way too long worksheet on various properties of the evolutes of the ellipse, and one of the last things I did was make animations of these curves which are a fixed distance along the normal lines, which develop singularities along the evolute. Very cute and so reachable from elementary calculus with a tool like Maple.  [<a href="http://www3.villanova.edu/maple/misc/frenetellipse.htm">www3.villanova.edu/maple/misc/frenetellipse.htm</a>] This is sort of like optics but in physical optics you have to recalculate the new normal at each successive curve to get the wavefronts, not continue along the original normals. But still it gives a flavor of what happens in optics. The latest comments added to the Blog Entry, It's Better With Maple 35276 Fri, 19 Mar 2010 22:43:03 Z Dr. Robert Jantzen Dr. Robert Jantzen Nice article. I was wonding if you (or someone) could derive the "intersec... http://www.mapleprimes.com/maplesoftblog/35171-Its-Better-With-Maple?ref=Feed:MaplePrimes:It's Better With Maple:Comments#comment35305 Nice article. I was wonding if you (or someone) could derive the "intersection of the line normal to the graph of <img src="http://mapleoracles.maplesoft.com:8080/maplenet/primes/9CE7D1C0CC53D7248F7ECB26AB5B2CC4.gif" alt="y=x^2" align="absmiddle"/> , namely <img src="http://mapleoracles.maplesoft.com:8080/maplenet/primes/94A224F8178BC340AA77B0FD0521193E.gif" alt="y=a^2-(x-a)/2/a" align="absmiddle"/> rgds The latest comments added to the Blog Entry, It's Better With Maple 35305 Sun, 28 Mar 2010 14:01:44 Z Poida Poida At the point on the graph of the parabola , the equation of the normal line is ... http://www.mapleprimes.com/maplesoftblog/35171-Its-Better-With-Maple?ref=Feed:MaplePrimes:It's Better With Maple:Comments#comment35310 At the point (<img align="absmiddle" src="http://mapleoracles.maplesoft.com:8080/maplenet/imaging/image?maple=x" alt="x" align="absmiddle"/>,<img align="absmiddle" src="http://mapleoracles.maplesoft.com:8080/maplenet/imaging/image?maple=x^2" alt="x^2" align="absmiddle"/>) on the graph of the parabola <img align="absmiddle" src="http://mapleoracles.maplesoft.com:8080/maplenet/primes/9CE7D1C0CC53D7248F7ECB26AB5B2CC4.gif" alt="y=x^2" align="absmiddle"/>, the equation of the normal line is <img align="absmiddle" src="http://mapleoracles.maplesoft.com:8080/maplenet/imaging/image?maple=v%20%3D%20-%28u-x%29/%282*x%29%2Bx%5E2"/>, where <img align="absmiddle" src="http://mapleoracles.maplesoft.com:8080/maplenet/primes/C93CB52769A7751BD8A27DE67E3E410D.gif" alt="u" align="absmiddle"/> and <img align="absmiddle" src="http://mapleoracles.maplesoft.com:8080/maplenet/primes/A9D26770FCD6656FB2DF0788367F0734.gif" alt="v" align="absmiddle"/> are the coordinates of points (u,v) along the line. If points along the normal line are to be expressed as (x,y), then points along the parabola have to be parametrized differently. For example, along the parabola the generic point could be (<img align="absmiddle" src="http://mapleoracles.maplesoft.com:8080/maplenet/imaging/image?maple=a" alt="a" align="absmiddle"/>,<img align="absmiddle" src="http://mapleoracles.maplesoft.com:8080/maplenet/imaging/image?maple=a^2" alt="a^2" align="absmiddle"/>), in which case the equation of the normal line through this point would be <img align="absmiddle" src="http://mapleoracles.maplesoft.com:8080/maplenet/primes/8CE4A3D9ED9DE7BFF5E0354EB20C33BF.gif" alt="y=-(1/(2*a))*(x-x)+a^2" align="absmiddle"/>. In either representation of the line, it should be clear that the point-slope form was used, with <img align="absmiddle" src="http://mapleoracles.maplesoft.com:8080/maplenet/imaging/image?maple=m%20%3D%20-1/%282*x%29"/> being the negative reciprocal of <img align="absmiddle" src="http://mapleoracles.maplesoft.com:8080/maplenet/imaging/image?maple=diff(y(x),%20x)%20%3D%202*x"/>, the slope along the parabola. The latest comments added to the Blog Entry, It's Better With Maple 35310 Tue, 30 Mar 2010 22:26:03 Z Robert Lopez Robert Lopez Wonderful solution http://www.mapleprimes.com/maplesoftblog/35171-Its-Better-With-Maple?ref=Feed:MaplePrimes:It's Better With Maple:Comments#comment104146 I can't help myself saying that it is a really wonderful solution by using arc length integral to derive the parametric representation of the curve parallel to y=x^2. Best regards. The latest comments added to the Blog Entry, It's Better With Maple 104146 Tue, 12 Apr 2011 19:16:09 Z Wang Gaoteng Wang Gaoteng