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Calculating the Shortest Distance from an Ionosonde to a QSO Path Using Sage, Cross Products, and Geometry

 I've run into an interesting math problem. Project TouCans occasionally makes dx contacts. That's not a problem, that's actually really awesome! However, KO6BTY and I would like to be able to map the F2 skips our radio signal makes on its way to the receiving station. We have plenty of data about the F2 layer of the ionosphere that is captured by ionosondes around the world. The issue is how do we determine which set of ionosonde data to use? Our first guess is that we should use the ionosonde closest to the path of the signal at any point. OK... Now, how do we determine that? First, we'll calculate the shortest distance from each ionosonde to the path of the QSO between ham radio stations. Then, we can sort the distances so that we can only include the ionosondes that are closest to the path. Armed with that data, we can perhpas used the distances to calculate a weighted,  estimated height of the F2 layer at any point along the signals path as it skips from ...

The Short One: Lab Book 2014_07_31

Summary: The day felt productive!  Honest!  However, looking back at the lab book, it doesn't look like a whole lot happened.  It could have been the two meetings sandwiching the beginning and end of the day.  Anyway, here's the cool stuff that did happen.  After fretting for a bit about where to get more computer time to run simulations on the can crusher code, I tried out  +The SageMathCloud .  It's so cool!  The simulator runs a little bit faster than my laptop and without out all the incessant fan blowing!  In addition, I can setup simulations in parallel, something I couldn't benefit from when limited to my one local machine.  The simulator proper has been partitioned into its own file.  The simulations are now much more manageable, containing only setup parameters and results.  One new feature was added to the simulator.  The driven can modeling coils can now be made superconducting.  I'm not sure I trust...

SageMath, Where Objects Rock and Scripts Don't

I moved the Sage simulation of the can crusher to an object oriented implementation today.  A few days ago,I was worried this might have been a bit of overkill and just a subconcious desire on my part to place the project in a code format I'm used to seeing things in.  I hit an example yesterday that convinced me otherwiser, and only a few short, OK,  and somewhat grueling, hours later, I had a much easier to use OO simulator. Prior to yesterday, my usage mode of the can crusher code was as follows: 1.  Evaluate the cell that contained the initializaiton code.  There were some declarations of global varaibles and a little bit of code that atually ran on evaluation to place values in these variables. 2.  Evaluate the cells that contained the current calculating function and the can moving function separately. 3.  Evaluate the cell that contained the simulation code. This, as far as I knew had to be done every time I wanted to change any values a...

Cuneiform to Computers and the MAA Lattice Points Problem

Imagine living thousands of years ago in ancient Sumeria as a mathematician.  Your medium for storing infomration is cuneiform on clay tablets.  As you work, you stamp each equation into wet clay by making wedge shaped marks using the blunt end of a reed to make a finished document that looks like this (picture 1)[1] When your instructor tells you to investigate the properties of a table of let's say, a hundred numbers or so, you might sigh in resignation, and plan on having results by sometime next week. With the advent of paper and pencil, things become much easier.  There's still lots of work to be done, but the recording of the information so that it can be viewed and worked with is, comparatively speaking, a piece of cake. Finally, though, the computer comes along and getting a table of 100 numbers is more like playing.  With  +The SageMathCloud   the 100 number task suggested in the +Mathematical Association of America  video below...

The Alcubierre Drive's Tophat Shift Function In Motion

The Alcubierre drive works, (theoretically), by warping space 'downwards' in front of a spaceship and 'upwards' behind it, (picture 1). The net effect is that the spaceship always feels like it's free-falling through space.  We have to be careful not to let the spaceship approach either the upward or downward walls of the curved space shown above.  In these regions, gravity due to the curvature of space is changing rapidly, and will cause uneven forces, known as tidal forces, on different portions of the spaceship that can cause it to break apart.  That's where Alcubierre's tophat function comes in.  The tophat is the input to the operation that describes how space is warped by the drive.  It's nice, flat top becomes the flat area in the middle of the warp shown above where the spaceship can safely rest. In case you weren't there, here's the description of the tophhat function I provided in the last post on the Alcubierre drive [1], (s...

Embedding Sage Cells in HTML Pages

Update:   I finally found what looks like very complete documentation on the Sage cell server . I'm taking a little break from the Alcubierre work [1] and jotting down a few notes on how to embed  +Sage Mathematical Software System  cells into html pages.  I couldn't find any documentation or howto pages for this, so here are my instructions for the next time I get ready to do this. Insert Sage Javascript at the Bottom of the Page For whatever reason, my blogspot entries will erease code placed at the top of a post.  They will however allow scripts that are included at the end of the page, go figure.  So, at the bottom of the page place the following html code: <script> $(function() { sagecell.makeSagecell({ inputLocation: '#graphdemo', evalButtonText: 'Analyze the Alcubierre tophat function'}); }); </script> In the position on the page where you want your actualy sage cell to be displayed insert a div wrapping your sage code...