Updates
The project for a simplified Fourier analysis of guitar string harmonics; Mathematics 1 is on hold while I update the main animation sequences to keep up with changing times.
The main sequence update progress can be checked out at New Design and Immediate Update Issues.
July 27, 2010
1. New Segmentation. This combines and revises all the original animations at about 1/3 the file size. It is not optimization for Mobile which is likely to require programming skills I do not have but it is a step towards simplification.
2. Modified Fretboard, Circular Functions 2, Circular Functions 6.
3. Modified New Design to change Segmentation Animation.
July 24, 2010
1. Modified Introduction
2. News from Indian Government, last Thursday they unveiled a $35 touchscreen tablet prototype aimed at students, with optional solar power for a bit more money, memory card instead of hard drive. Keywords "Kapil Sibal", "Economic Times". No manufacturer yet.
July 21, 2010
1. New Animation Math Idea . Nothing really new. This is a review and revision of the ideas I was working on several months ago and had to drop when the Ipad came out without Flash.(July 21, - Added this to the download since yesterday.)
The main animation sequence is clearly in need of some update in line with increasing mobile platforms and competing technologies and general outdatedness.
Circumstances may require some changes in approach - reviewing the New Design animations indicated two or more weeks work so to fill in a day or so of time this math idea has been put into a slightly better form.
2. Updated mathematics_052810.zip , 2 mb, unzips to 10mb. Added Math Idea , Corrected Title link and Back to Top of Page link.
3. Minor update of Miscellany to a more uniform "default" text.
July 17, 2010 (3rd revision)
1. Modified Introduction.
2. Modified Fretboard.
3. Apparently, a keyword I should be looking at for some sort of universal schoolbook platform is "smartbook". See:
An important issue for me, whether Flash 10.1 will work on them...it is now being tested- by others.
4. Modified Immediate Update Issues
July 11, 2010
1. Modified Introduction. So far just a few minor changes in verbiage.
July 10, 2010 (2 corrections in the last 3 days)
1. New Introduction An idea or two on how to enter the main animation sequence.
2. Modified Fretboard - A problem with the page menu button was corrected.
3. Contents - added link to the Quick Time video "Mesolabium" 277kb, 1.0 seconds it is now H264 and will play in the Ipad when the Apple QT plug-in is downloaded. I might try to improve it but at least for now, anyone on the device can get a quick idea of what the Musemath Flash content is all about.
The trade off seems to be between battery life and file size (cost of data transmission).
4. After visiting the Ipad and the 21+ inch Imac at the Apple store, went over to the Microsoft store next door and viewed the HP TouchSmart tm2t 2952 laptop/convert to tablet with stylus. An i3 computer, pretty good specs 9.5 hrs battery (heavy video and Flash will get significantly less) - no CD/DVD, I'm told they are heavy drain on battery - plug in external when needed. 12" screen, good keyboard. A computer and so apparently a better school choice than the high end Ipad (I pad so far is a better entertainment/surfing device 1 + lbs. weight) - Touchsmart is $900 - any student discounts and 4+ lbs weight.
Some more on this kind of device:
TouchSmart tm2t
Still nowhere near the $100 laptop per child or even the $250 netbooks possibly affordable worldwide (if they have any durability). Checked out OLPC again to see how they are doing.
Since Musemath is concerned with science and every kid in the world has to learn this subject the same way, the lowest common denominator is an affordable delivery system. Content can be devised around that criteria with an eye to what these higher end systems may be able to deliver into the future. The principle concern is imagery which is cross-cultural, platform independent.
OLPC apparently intends adding touchscreen functionality at something over $150 in a few years and eliminating the physical keyboard in a later tablet version.
Apparently, their current devices should play most if not all of the Musemath animations as is and I have downloaded and am now trying to figure out how to test in their default "Gnash" player.
5. The problem I encounter on the new PC's especially is that my Flash animation buttons are a little too quick, they skip pages etc. Interesting, will look up any solutions. Musemath Flash animation buttons do work by touch on the HP Touchsmart - will have to see if they are practical on more mobile devices.
July 4, 2010
1. Revised Vectors Replacement - This is still a placeholder as far as I am concerned, more math and physics will be needed to complete - possibly October - it is sufficient as is to enable the intended New Design format which is the priority.
2. (Revised) - Quick Time video "Mesolabium" 277kb, 1.0 seconds it is now H264 according to Flash export. I only had a few minutes to try the Final Cut solution noted below and did not succeed with it. It might take a few days before I can get to an Ipad to see if it works on the targeted device. It is only intended to give some idea as to what the Flash content is like.
June 30, 2010 (#2 modified July 1)
1. (Revised since yesterday) Vectors Replacement - The current animation has been nothing but a placeholder for many years. This needs more work but an improvement nontheless. It is now over 100 kb since I have added a screen shot from the Falstad applet. my thinking is that if plug-ins are not available on some new devices, and html5/canvas/svg is not yet up to the task, this proceedure may get some of the information into viewable form - at least an idea or two for the layout.
So far as the vibrating string, I find the Falstad applet easier to work with since it has more variable inputs. Will leave a reference to the Ord page as there is some explanation there of analogies to more advanced physics that may be of interest to some.
2. (Removed July 1, 2010) - Quick Time video "Mesolabium" 1mb, 2.6 seconds. There is a link from the Contents page so those browsing on a non-Flash enabled device can get a quick idea of the type of animation covered here
When tested on the Ipad at the Apple store this wouldn't work - probably not a new enough H264 version - possible fix here: http://www.mediastorm.com/blog/?p=2137
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June 25, 2010
1. Modified Fretboard - This seems to have more potential than I had originally thought.
2. Minor correction to Dienes Multiplication , p2.
June 24, 2010
1. New Fretboard - This will put all the frets and frequencies and interval ratios into order after a bit more work.
1. Two days old Octave Test - An idea which may replace one or more of the current animations. The temporary name comes from the fact that I wasn't sure if it would work for an octave interval, and am still not sure it will be able to demonstrate that (or smaller intervals) in any useful way.
2. Modified Kinetic-Potential corrected a rather obvious labeling error by reversing the border on the Definition boxes and reversed the guitar position.
3. I did make a quicktime video of a small part of an animation with the Mesolabium demonstration. I was rushed for time (learned to use the setting for duration rather than the one for last frame which didn't work) - It was only a small part of a 50 kb flash animation but converted into a 2.6 mb video file. It is functional but would require some more editing to make it into a worthwhile promotional video.
Will try again to make something a bit smaller and better.
June 19, 2010
1. New Wavesums_1_New - May revise eventually but at the moment, I'm just trying to figure out what I did when creating this one. It is probably functional as is and optimizations may come later.
2. Third revision of Wavesums_2_New
June 18, 2010
1. Second revision in two days of Wavesums_2_New a number of issues to be resolved.
May be able to combine both the current Wavesums animations.
Interesting, page 4, ""Traveling Waves 2" is actually my very first animation and might make a better introduction if I can work with it a bit more.
The standing wave idea is an analysis from the traveling wave idea so the priority is better and it is simpler in appearance. Some difficulties caused by my "Newbe" status at the time of creation (November 2002)
2. Modified New Design to include the above.
June 15, 2010
1. Sixth revision: Temperament_New_Format
June 11, 2010
1. Fourth revision in as many days: Temperament_New_Format - discovered a few problems and fudged a few frames of the animation on page 2 and 4. It seems likely this cannot be made too precise if it is ever to play with a reasonable frame rate in anything like a "Canvas" animation in the near future. A good mathematics - CAD program might do better but for the moment, Flash 8 will have to do here. Will probably try to refine it.
2. Did get to the Apple Store in Fashion Valley. The IPad looks like a very good innovative web magazine format to me, that's all many people want so a very good tool for mass marketing. With potential for more.
Tried to see some of the animation capabilities but it was so busy marketing itself I couldn't quickly find any free samples to test.
It does reach the internet very well, navigates exceptionally well, zoom in is great, and it is certainly a pleasure to not have to worry about browser crash or annoying animated advertisements.
Some bloggers are indicating it is good for limited business matters but indicate the need for add on bluetooth tools. Possibly they just want the device. I did, though I believe a book, note or net, would be more practical for my goals and budget today. Without the interactivity of Flash, applets and other interactive programming, it is inadequate to much current science e-learning.
For Musemath, I will rewrite some of the HTML pages - less wordy. Also, when an animation is clicked, though it does not populate, there is a good opportunity to explain the purpose of the animation and describe what it shows. (2-3 short sentences).
As for what to actually buy, took another look at the 20 1/2 inch imac. They have Flash CS4 loaded (interesting, not conclusive of anything) and my downloaded Ratios 3 animation exported to Quicktime but I had failed to get it animated. Will try again - it may be that the limited interactivity of replaying short Quicktime movies is a temporary solution for Ipad.
3. A few more posts on current Flash status:
http://thomastalkstech.com/blog1.php/world-browser-war-iii-html-5-vs-flash-fl
"Will HTML 5 allow me to create the unique, interactive learning experiences that I build in Flash?"
"Flash is a great tool and the files it creates display the same in every browser on every platform. The inconsistencies in the way the browser displays content has no impact on your .swf. It runs the same, it looks the same, it feels the same, and it sounds the same on each and every platform. It is a stable tech that my clients understand and provides me with creative flexibility."
"As an eLearning developer I feel it’s a great opportunity to get into learning the new languages like Objective-C and HTML5 which has now become mandatory because of Apple’s policy. But at the same time it’s a huge investment for eLearning vendors to train their workforce on these new languages so that they can develop the iPhone/iPad apps and that too without being sure of iPad or iPhone would be big in workplace learning domain at all."
June 6 , 2010
1. Revised:Temperament2_reversed_4.html Possibly adequate for the moment.
Page 2 has an unrelated note on the Derivative concept I wanted to sketch out before forgetting it, the formal presentations I have seen so far all refer to slope and my response to date had always been "so what, why, how, etc."...thereafter, "who cares? " It has not been a major study since I am thinking of Fourier as integration and integration is the introductory concept for calculus used by Courant Robbins.
The idea may not be correct but it is an idea of how to understand the subject and generates some interest - worth more than the subject itself. I will open up the Stewart and the Anton though nothing will be persued in detail untill the preliminary math is reviewed.
June 4 , 2010
1. New animation - despite the temporary name, it has turned out as more of a revision of the current "Aesthetics" animation. Logarithms1_1_New_Format.html
The image juxtaposition on the first page seemed a good idea so I just took it where it wanted to go - a lot of ideas had been accumulating. Flash is probably not the best format for all the verbiage on the remaining pages but it does help to fit the concepts into a condensed unified whole, (like a sonnet). At least it is selectable now.
There is room for a bit more and I don't wan't to finalize things till all the imagery is finished.
Now to get back to the cause of all this:
Temperament2_reversed_4.html
Which is a "beta wanna be" and causing some difficulty, a lot of things here don't reverse direction very well.
May 31, 2010
1. Minor modifications to title button for greater consistancy in Integration 1-3, Nested Intervals, Number Line, Secant, and Sum of First "n" Squares.
2. Nested Intervals: page 2 - removed the alpha motion transparency from Berkeley's Ghost as per Adobe optimization recomendations by putting it in a lower layer at 100%. With a bit more work the mask effect may be eliminated as well. May want to code "_visibility = 0" instead of just inserting a blank keyframe.
Optimizations remaining:
Math Animations with Motion Alpha Transparencies
Number Line (p7 Venn Diagram and Venn to Continuous Number Line)
Nested Intervals (p5 "Berkeley's Ghost") partially done - need to remove mask
Integration 1
(pp2-4 yellow zoom-in circle)
(p 19 limiting sequence of red rectangles)
(p20 possible - area under curve?)Integration 2
(diagram has stationary alpha transparencies )
(p6 possible motion transparency to math symbols and fade outs which should be reprogrammed to _visibility = 0)
(p8 Foil highlight transparencies)
3. Mathematics 1 - corrected a link.
May 28, 2010
1. New Download mathematics_052810.zip , 2 mb, unzips to 10mb. So that the ideas and formatting are available to all while I am working on the main animation sequence.
May 26, 2010
1. Modified "Logarithms 3". (2x) Still experimenting, still need a bit more research.
May 22, 2010
1. Started a new "Logarithms 3". Rough draft, removed some of the alpha motion tweens as suggested by Adobe Best Practices, it is missing a bit of continuity at the moment. Will next test reversing the direction of the guitar and adding in some other logarithmic material.
Each stopped note is a function of the open (whole) string length. My current thought is that measuring from left to right will cause less problems of interpretation with some of the mathematics later on.
However, fret numbering would then be from right to left and the frequency curve will be one of decay (this is not the way I think of the guitar when I play). Not sure yet, no perfect solution but I want a consistant imagery and need to work with it a bit before changing all the rest of the animations.
2. Removed the header links from all but the home page...seemed a bit too many simultaneous multitasking options. The multiple buttons and limited flash navigation being used is difficult enough as is.
May 20, 2010
1. Modified Home Page. I was trying for a non-liquid, center or left column design - suitable for the mobile smart phones - didn't get it. This may work for now, at least the links stand out a bit better and its a bit brighter overall.
I do not really know when or if smartphone users will want to use the site (it is currently all mouseclick interactivity). However, it will show up in those devices which use search and it should be simple and self explanatory to encourage later use on another device.
This liquid design seemed to work ok on a Blackberry some time ago. I expect there are problems with some the tables on other pages.
2. Researching logarithms to revise the animation Logarithms 3 into the new format.
May 17, 2010
1. Rework of Third Partial . First Draft, principally to test the effects of reversing the direction of the guitar image as per Immediate Update Issues.
May 16, 2010
1. Modified Circular Functions 2. 18fps and pages 7,8 showing complex circular motion generating the complex longitudinal wave.
2. Temporary file Immediate Update Issues which is something of a to do list and restatement of current goals.
3. Minor link correction to Mathematics 1.
May 13, 2010
1. Modified Circular Functions 2. 24fps - The rotations are now counterclockwise and come to a stop. An interesting aspect of phase and wave direction has been added. The relation between waves and the string still needs to be addressed. Some of the animation does not work as smoothly as it used to despite higher frame rate, but it may be more functional on some of the mobile devices. Not sure yet. Will probably leave as is and work on something else, logarithms?
2. Found the following Apple app info which is topical (physics - waves) and gives me some idea of what is currently being done over there.
http://physics.bu.edu/~duffy/iPhone/waves/waves.html
Link to the PhysicsWaves app on iTunes
http://www.itunes.com/apps/PhysicsWaves
3. Following link on Canvas and its future:
http://www.slideshare.net/robhawkes/html5-canvas-the-future-of-graphics-on-the-web
Also Googled "html5 vector animation gui"
Apparently they are two different things, Canvas is bitmap, don't quote me, I'm still trying to figure it out. Looks like nothing in my category yet.
4. The Apple/Flash made the news again on a love note advertisement taken out by Adobe. I want to check it out even though the rants and comments are not always very helpful. I'm trying to develop content for whatever medium can get it distributed (same as everybody else) and have to make some guesses as to what the options will be.
The only way I get any work done is to go offline for a few days at a time. Going through my old animations can be frightening, certainly tedious, I need some surfing, I sure hope some of the sites work.
Some earlier material follows, I'm still looking for a place to put it:
Eolas blarney is still in business, will keep this link as a reminder:http://news.cnet.com/8301-30685_3-10368638-264.html
http://www.wolframalpha.com/ 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.
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."
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."
Another possibility at: http://krisjaydesigns.com/?p=252
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 commercial 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