Updates
Since roughly the end of May, 2008 this has been pretty much a demonstration of how I am learning Calculus for the eventual purpose of a simplified Fourier analysis of guitar string harmonics. To date, the three HTML pages: Mathematics 1.html , Mathematics 2 .html, and MathWebsites.html contain the notes and references being used for the project, including links to the new animations. I try to keep a two month chronology below.
March 11 , 2010
1. Tried to change the Contents page to pure html. This will give me more room to work and insure that anyone without the flash player actvated can see what is available if interested. Some more work will be needed.
2. Removed the animated gif from the home page - it was no longer appearing correctly on Internet Explorer 8. It is now a static image.
March 8 , 2010
1. New Zarlino this contains two images and some probable connection to Descartes' La Geometrie. I had first seen the mesolabium image at youtube: http://www.youtube.com/watch?v=KbKkfqCFy0w and after some research, noted some superficial resemblence of the page one image to Descartes "proportional compass".
2. Mathematics 1- (above animation added), brief comments added to Design, and Future .
March 6 , 2010
1. Modified Fourier 3 and will probably leave it as is for a while. Some of the older movie clips are going to take some work and I am not yet satisfied with my own mathematical background here so some more study will come first. Nevertheless, it shows the kind of approach I think would make the subject more accessable though it will not of itself develop proficiency and skill
2. Rather appreciated the following definition of mathematical elegance from Prof. Joyce. in his online, Euclid's The Elements.
http://aleph0.clarku.edu/~djoyce/java/elements/bookI/propI30.html#guide
"Elegance in mathematics is characterized by simplicity and clarity. An elegant presentation is easy for the reader to follow. But elegance is not only in the presentation, it is in the selection of definitions and proofs. The elegant definition is the one that makes the rest of the theory easy. The elegant proof is the one that is easiest to follow, one that is designed just right to fit the goal. Extraneous concepts should not be involved. Even the goals need to be adjusted to the right level of generality to cover the concepts, but not so abstract that the abstraction itself obscures the goal."
3. Will work a bit more on some basic arithmetic ideas. Division specifically - that's the wherefore of the Euclid.
March 3 , 2010
1. Took another look at Fourier 3 and made some modifications and additions. Surprisingly, it is beginning to take shape and I think I will be able to make it into some sort of popular presentation, sufficient to convey the idea to an interested guitarist at any rate. First time I have some confidence on the goal. Only two days late for the last deadline (No new deadline, it is still crude, some of this needs to be thought through and some detail on preliminary material should prove well worth the effort).
February 28 , 2010
1. No really good Fourier animation will be available tomorrow, every time I work on it I see some preliminary work that seems essential to any decent presentation. Will take some time before coming up with a new target date.
2. Revised
Complex Numbers (link on page 5)
Ratios 3 (Pretty much converted to a work on Descartes since he seems most responsible for the current understanding of the relation between arithmetic, geometry and algebra as it is taught in general grade school and I think he deserves a bit more credit than he usually gets for having thought through and accomplishing his goals at the time and under the conditions then existing - Inquiition, Galileo, 30 Years War, etc.) There is quite a bit more animation to do.
Euclidean Algorithm 2 - minor typo correction page 9.2
Fourier 3 - This is really an advanced topic, if I try to complete a popularization without some more advanced understanding and just general knowledge I might do more harm than good. It is incomplete and in limbo though I may work on it from time to time.
3. Finally got to the Mac lab (they have a new schedule and it has been difficult to get there) It turns out they haven't even bothered to update the Flash CS4 version (for what, 10 months?) and have left the CS3 version on the machine as well (there is a Snow Leopard issue that probably requires the CS3 but nobody cared to update the CS4). That tells me enough.And, I thought the original PC version was bad enough, this was worse, unworkable, the AS editor Auto Format intentionally screwed up the syntax - I did it 3x because I couldn't believe it. No password available so I couldn't run the update. Will try the Apple store again to see if they have an updated CS4 on the 27" IMac.
In any event, mobile animation and video is a big issue, lots of buzz and infighting for market share. CS5 is expected soon and there is currently no reasonable alternative to Flash authoring for nonprogramming people such as myself that I am yet aware of. Will probably go for some I-5 PC but will first try to get something other than sales pitch at the Apple Store, can't afford an expensive computer that doesn't run the program I need, regardless of responsibility or desirability.
Will keep watching developements - HTML5, Canvas, Silverlight, etc.
4. Want to check this site from Wolfram:
Making the World's Knowledge Computable
Today's Wolfram|Alpha is the first step in an ambitious, long-term project to make all systematic knowledge immediately computable by anyone. Enter your question or calculation and Wolfram|Alpha uses its built-in algorithms and a growing collection of data to compute the answer. Based on a new kind of knowledge-based computing...
February 21 , 2010
1. Modified Euclidean Algorithm 2 animation again at last check it was working fine on a netbook that was using external power.
2. I'm trying out a fix on the home page for the Internet Explorer 8 browser:
<meta http-equiv="X-UA-Compatible" content="IE=EmulateIE7"/>
see: http://msdn.microsoft.com/en-us/library/cc817570.aspx
"This will tell Windows Internet Explorer 8 to render each page as Windows Internet Explorer 7 would, fixing your Web site."
I expect this will be required for each page but first will make sure it works. Will have to get back to the store where the new netbooks are running Win 7 and IE8.
Another possibility at: http://krisjaydesigns.com/?p=252
And who knows what other browsers may need.
3. I went to the Apple store and as far as they are telling it, Flash is already dead and buried. As usual I enjoyed the visually sensual feast of the Macintosh monitors (27") and had the pleasure of petting the magic mouse. They did have an Adobe CS4 suite loaded and Flash was working apparently.
From the education world, specific perhaps to the IPad:
"But my $300 netbook does more than this and has multi-tasking, Flash support, a real keyboard, support for peripherals, and millions of apps."
David Andrade
I am a Physics teacher and educational technology specialist in Southwestern, CT.http://educationaltechnologyguy.blogspot.com/2010/01/apple-ipad-is-it-game-changer.html
4. At the other electonics store I tried out a Toshiba 10" netbook with raised keys that were easier to type with than any of the other netbooks - but with a $400 price tag. Some problem with Full Screen interfering with my animation buttons Again, the last XP - IE7 worked but this Win7, IE8 causes problems - something else to be considered.
Animations worked, a bit small without Full Screen I may need to reconsider javascripted windows or placing the animation navigation on the side.
February 18 , 2010
1. Modified Euclidean Algorithm 2 animation again, a new page 9. This one actually shows the analogy for the algorithm.
1. This site by a "Platform Evangelist" seems a reasonable point of view from Adobe on mobile internet:
http://theflashblog.com/?p=1758
February 14th 2010
Lee Brimelow is a Platform Evangelist at Adobe focusing on the Flash, Flex, and AIR developer communities.
February 15 , 2010
1. Modified Euclidean Algorithm 2 animation again, a new page 8, still experimenting with the size and clarity.
2. Revised Complex Numbers animation - added a new page 10, also revised slightly Ratios 3
3. Some corrections will be needed to the History section and the animations on the Mesolabium. I will note them here and make the actual corrections a bit later.
a. There is a youtube video (in Spanish) on the Mesolabium by Carlos Calderón Urreiztieta. which apparently includes some illustrations from Zarlino's 1558 book, especially the illustration at time 0:52/3:46 http://www.youtube.com/watch?v=KbKkfqCFy0w
The information I had (from Barbour p50 I believe) was that Salinas had recommended use of the instrument for 12 Tone Equal Temperament after reading the 1558 book and that Zarlino followed that advise in a later book 1588. There is some indication or speculation that this particular illustration was influential upon Descartes' development of algebraic curve drawing devices. The analysis of curves being of importance in calculus, and further, this apparently being the first published illustration of the geometric derivation of Equal Temperament at least in the West, it seems worth verifying the date of this illustration.
b. My own animation had been based on later verbal descriptions and illustrations of simpler instruments and in fact there seems to be something wrong with my math.- possibly based on what appears to be a fairly common misunderstanding of a difference between logarithmic and exponential series.
c. I expect I will need to make revisions to:
1. Fourier 3 page 5
3. 12 Tone Equal Temperament/EDO Tuning History Timelineat 1558, 1577, 1588
4. Some sort of correction to the downloads.
4. Some further research indicates the problems with Apple and Flash may have more to do with who gets control of Mobile Online Video than with cpu usage by Flash animations. Difficult to be sure, a lot of hype, but Flash will use up battery life quicker than a static page. I put a notice on the home page. And, Adobe posted a pdf beta version of Flash "Optimizing Mobile Content" on February 12. A few things I can address such as minimizing alpha transitions - possibly some memory issues - changing movie clips back to shapes, etc. - most have to do with programmers optimizing code for hand-held devices and it doesn't appear that I will be able to do that at this time. It seems that in addition to the battery/power consumption issue, the processors for hand-held devices are inadequate to some of the more complex animation techniques. I have seen my animations working pretty well on Netbooks when they are plugged in to external power sources and believe that is an essential condition, limiting but not eliminating their use in education. Flash and Java Applets are pretty much the norm in education today, the Apple Tablet may yet adjust for this market and indicate how to get similar or better interactivity features. I believe hand held devices to be beyond my current capabilities, will keep an eye on this.
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February 8 , 2010
1. Modified Euclidean Algorithm 2 animation again creating even more problems for myself, but I think it worth investigating a bit closer and so will spend more time here. Page 2 is I think worthwhile to show now - all is ad hoc.
February 2 , 2010
1. Modified Euclidean Algorithm 2 animation but ran into a number of problems most of which are self evident and/or explained in the animation. (very minor correction from yesterday, the major problems here will take a few days).
2. Revised date for a basic Fourier Animation - March 1, 2010.
January 30, 2010
1. New, Euclidean Algorithm 2 animation - also revised slightly Ratios 3 ( it will replace Ratios 1 and 2 eventually) and Irrationals. These are all preliminary trying to create and fit all the needed imagery wherever I can. In a bit of a rush to start and now a problem has arisen. The February 1 deadline for the Fourier animation is not dead yet but realities may set it back one month.
2. As rumored the Apple Tablet apparently will not show Flash, at least not to start. As I understand it, all the Flash advertising makes a mess of battery life and makes a lousy viewing environment anyway. Jobs looked like he was enjoying himself which is not always true of the surfing experience even on desktops. BUT, to replace these Flash Musemath animations with bitmap animated gifs or something would apparently increase filesize and bandwidth usage enormously - perhaps 50 times filesize and interactivity would be seriously reduced as well. I researched a few Apple Apps such as Flipbook and Flickbook, they reminded me of the original vibrating String animation I did on a PDA application which eventually turned into the Temperament 1 Animation. Nothing yet can replace the ability (especially for a non-programmer) to layout and publish interactivity as well as Flash. I watch the business pundits on TV as they keep abreast of things fairly comprehensively and try to explain in non tech terms, also I did some selling of the initial Sprint cell phone launch from back in the days when mobile internet was a tough sell in the United States (Why would you want to connect to the internet from a phone? - incredible). I'm not at all sure where this is all going but there is some balance between cpu, memory, bandwidth (I had thought they were going to start charging for bandwidth by this time...no doubt they want to get us all thoroughly addicted first), exclusive sales rights to apps, and dependable cost effective hardware that needs to be considered in education as well as entertainment. I visited the Apple Store (the physical version) in Fashion Valley to nose about some (not much info yet) will probably make a few more trips to see what I can find out.
Adobe has been making Flash more adaptive to mobile use but not yet to the standards of Apple (read Jobs) and there seems to be some issue that Flash could bypass the Apple App Store as well. Hard to say, everybody adds their own spin to the top when money is at stake and nothing is static in internet usage.
Some Internet material:
http://www.guardian.co.uk/technology/2010/jan/27/apple-ipad-announcement-live-updates
Apple isn't trying to replace Flash with its own proprietary thing. They're replacing it with H.264 and HTML5.
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http://www.internetnews.com/dev-news/article.php/3842291
...Steve Jobs has publicly criticized Flash technology, saying it's too slow and inefficient for mobile devices
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http://www.kaourantin.net/2008/09/on-performance.html
It takes CPU cycles to decode video, sound and render animation. This is just a fact of life...
No doubt there is more to come.
Since this is a family website, though disappointed, I will not be adding any color to the off color humor surround the unique naming of the Ipad though color is inherrent to my thoughts on the matter. Its a good looking device something constructive should come of it.
In the meantime I am thinking of education as requiring mobile devices to be plugged in to external power sources in school and at home with some limited battery use of cpu intensive interactivity such as Flash (optimized). Today, Flash is irreplacable to me in laying out these ideas though I keep looking for a replacement.
3. While at Fashion Valley I went to see "Avatar", in addition to the usual meaning of "Pandora" which might have unintended implications to the off color humor noted above, Websters Collegiate also defines it as a "3-stringed lute" which might profitably be spun as harmony considering the message of the movie, in fact the lute is traditionally symbolic to harmony in European Renaissance Art.
It was also $3 for the 3D glasses - no doubt to emphasise that point.
January 26, 2010
1. New, Fourier 3 animation - it is preliminary but I thought I would put up some hints and rumors about what it might look like - works for Apple. It might actually look like something worthwhile by February 1 but more work will be needed.
2. Modified the linked pages courantRobbins.html and calculus.html a bit, they are now called Mathematics 1 and Mathematics 2, more work is needed here.
January 17, 2010
1. Feeling much better - Revised Complex Numbers animation.
2. Revised Text File outline of plans: Fourier Goals: (deleted February 28, 2010 most of the goals were accomplished but the animation I want is still eluding me.) Two week to go but at least now I can take a good look at the organization and realities of the February 1 deadline.
January 14, 2010
1. Not improving from illness as much as I had thought, tired, little concentration, some judgement issues, spent the last couple of days trying to do something besides onionskining a copy of :
http://paws.kettering.edu/~drussell/Demos/Fourier/Fourier.html
Fourier composition of a sawtooth wave
by Dr. Dan Russell, Kettering University
No success or I would link it now. And I don't feel like organizing anything or doing any math at all. Dissapointing so far as my February 1 deadline - I may be learning something from my mistakes but at the moment there is not much to do about it.
2. A broken link to : Eigenvalues and musical instruments by V. E. Howle and L. N. Trefethen on the http://www.musemath.com/miscellany/attackDecaySustain.html page was fixed by the addition of three new links which should keep it all reasonably up to date for a while.
3. Interesting review of the Intel Convertible Classmate PC http://techreport.com/articles.x/16496 and of course, like everyone else, awaiting Apple Tablet. Will it have flash support? and or educational features I want to cosider.
January 11, 2010
1. Not recovered from illness as much as I had thought, but improving. Text File outline of plans: Fourier Goals:
January 10, 2010
1. Bit of a problem, illness, fever broke 1a.m., RWI, recovery slow, I can now think again but three weeks is a bit short to come up with the improved fourier aimation for the main website animations. That has been the goal for some time now and I don't want to postpone it any further. Will set up a plan and checklist by tomorrow, what can be done will be done, will update daily, expect this to be very "messy", expect all comments between now and then will be deleted upon completion.
January 1, 2010
1. Modified the Tutorial. There are now 3 linked files, Tutorial 1, Tutorial 2, and Tutorial Supplemental which summarize some of the previous work which along with Generic Template1 and Generic Template 2 are all included in the general download:
This includes the previous work on Integration. This is all to make it a bit easier for the more mathematically inclined to put Flash content on the internet if they so chose.
Some earlier material follows, I'm still looking for a place to put it:
Regarding the Tutorial Download: (It is Flash 8, AS1 and 2 and can be opened and modified in the newer CS4 version) It's function will be to enable those Flash illiterati with mathematical ability to immediately produce respectable online tutorials, modules, etc. and to build on each others work with a reasonably consistant Flash Symbol Library.
Something like the following is in mind:
http://www.youtube.com/watch?v=gMdh_fiGZag&feature=related
Interesting graphics from the TV series "Mechanical Universe".
The Mechanical Universe contains hundreds of computer animation segments, created by Dr. James F. Blinn, as the primary tool of instruction..."There are about a dozen great computer graphics people, and Jim Blinn is six of them."
A number of videos from youtube on guitar string vibrations and resonance:
http://www.youtube.com/watch?v=JApds-f40m8&feature=related
A comercial for their software which is also a very good overview of resonance (concise and you might find it better than many more academic presentations) 2:52
Shows how SolidWorks/COSMOS can be used to find natural vibration frequencies of structures. What do they mean? How to avoid resonance.
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http://www.youtube.com/watch?v=eFXFkgqYkck
Guitar String Vibration photographed in high speed and then presented in slow motion video. It means high detail. You can see the things in a time space that you don't have in your everyday life. Please visit: http://www.engr.colostate.edu/~dga/hi... for more.
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http://www.youtube.com/watch?v=q9D6ceOWa3g&feature=related
DrDaveBilliards
June 01, 2007
Demonstration of the physics of guitar string harmonics and chords. Many more video demonstrations of engineering and physics principles and devices can be found at... http://video_demos.colostate.edu
Demonstration of the physics of guitar string harmonics and chords.
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http://www.youtube.com/watch?v=MtgPQQwkB4o&feature=related
3 or 4 repetitions of slow motion string vibration, center pluck
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http://www.youtube.com/watch?v=BBA32xnhE1Q&feature=related
1200fps (40x slowmotion) guitar strings as I strum them. pretty sweet. Playing with my new Casio EX-F1.
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Need to check out the link here -
String vibration simulation in Matlab with pdepe function.
http://physics-toolbox.trip... http://simulations.narod.ru/
animation - 16 sec - double pluck, initial condition includes both an upward and a downward disturbance from the horizontal equilibrium
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http://www.youtube.com/watch?v=-CrT-6VEtg0&feature=related
single string pluck 1x - 3:26 - 600 frames/sec
Some more leftover ideas with no place else to go:
themathpage.com treats multiplication as repeated addition but also links to a more general definition of it as a proportion and this is how I am thinking of it in the Dienes Blocks animation. http://www.themathpage.com/ARITH/multiply-fractions-parts-of-fractions.htm#def
3. Also, a link that might have relevance : http://cnx.org/content/m18052/latest/
First and foremost for me, a bit more general and unfocused algebra. It has become apparent that you can't tell where this stuff is going to pop up and there are commonly a number of different logical structures leading to various possible explanations sufficient (if not always optimal) to whatever the problem at hand. You can't tell much about what the person you are working with is saying, written or verbal, unless there is some common language between the two of you. Here, I understand the language of algebra from Webster's Collegiate 10th:
Algebra (Ar al-jabr - the reduction)...
2: any of various systems or branches of mathematics or logic concerned with the properties and relationships of abstract entities...manipulated in symbolic form under operations often analogous to those of arithmetic.
What is needed, as noted by Mary Boas, is not just superficial knowledge of the language obtained from reading and videos and passing tests; nor even the more exact knowledge I obtained by studied creation of the specific animations here.
It is skill in solving problems both new to me and difficult (for me) - that is being open to new ideas as they are presented and, as noted by Walter Lewin, such skill can only be obtained by having worked out similar such solutions for myself beforehand.
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An "Accessibility" pdf http://www.adobe.com/resources/accessibility/best_practices/best_practices_acc_flash.pdf
So far, with little practicalities ...presumably a greater percentage of overall audience loss. But, will keep in mind.
Googled "math for the visually impaired" to get some ideas for what's involved: Links:
http://www.tsbvi.edu/math/
http://mathforum.org/library/ed_topics/contexts_disabled/The webite includes a few links to a pbs.org site with interesting string animation (common strings and string theory strings.)
http://www.pbs.org/wgbh/nova/elegant/resonance.html
http://www.pbs.org/wgbh/nova/elegant/scale.html
"Anthyphairesis" A web page of interest is a record of an academic e-mail exhange on the subject, perhaps not originally intended for the WWW, and so not linked to within the animation...
A discussion of Greek mathematics St John’s College alumni unofficial email list begun 2004.5.31
http://74.125.155.132/search?q=cache:QeBvX8QrqQoJ:arf.math.metu.edu.tr/~dpierce/mathematics/Ancients/disc.ps+anthyphaeresis&cd=9&hl=en&ct=clnk&gl=us
http://arf.math.metu.edu.tr/~dpierce/mathematics/Ancients/disc.ps
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The utility of animation as a learning tool in mathematics is a principle concern. No doubt it can be of value throughout the subject though more so in introductory material and it may be an absolute hinderance with some or much of the more advanced materials. To be discovered, probably by someone else.
Found the following pdf document on school standards which may be compared with the Vels standards noted earlier.
http://www.utdanacenter.org/k12mathbenchmarks/downloads /secondary_strand_may08.pdf
Apparently derived from:
http://www.achieve.org/node/337
Achieve
Created in 1996 by the nation’s governors and corporate leaders, Achieve is an independent, bipartisan, non-profit education reform organization based in Washington, D.C. that helps states raise academic standards and graduation requirements, improve assessments and strengthen accountability.
Taking a closer look at the folowing site which has interactive Flash modules on Integration:
http://mathdemos.gcsu.edu/mathdemos/applicationsinflash/applicationsinflash.html
Objective: The goal of this demo is to provide instructors and students with interactive tools for approximating area under a curve and arclength using elementary numerical methods.
David R. Hill
Department of Mathematics
Temple University
The following two links seem well suited to my purposes here, they provide historical background on the coordinate system used so far:
http://mathforum.org/cgraph/history/index.html
Ursula Whitcherhttp://math.berkeley.edu/~robin/Descartes/accomplish.html Keren Zaks
Quick Quote for incentive to help keep me going:
J. PRESPER ECKERT
"A physicist is one who's concerned with the truth. And an engineer is one who is concerned with getting the job done and not with the truth." (PDF)
http://www.cbi.umn.edu/oh/pdf.phtml?id=245