Category Archives: Math on the web

Random walks around the web

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Here are a few noteworthy posts I’ve seen in the math blogosphere recently:

  • Denise at Let’s Play Math asks us to solve some chess puzzles.
  • Dave at Math Notations gives us a recursive sequence to think about.
  • There are two new problems at Math Challenges, here and here.

Funny Little Calculus Text

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Dr. Robert Ghrist, professor of mathematics at U Penn is writing a Calculus text–the Funny Little Calculus Text (FLCT for short). The FLCT not your typical Calculus text. Check out his incredible, artistic, funny, and mathematically elegant work-in-progress here. He currently has completed these short little chapters, all of which are a delightful read:

Ghrist lectures in a similar style, with a tablet PC. And yes, his handwriting is really awesome.

NOTE: I’m updating this post today (1-10-2013) because I’ve just noticed that Ghrist has placed these files behind a (very low) pay-wall. They are STILL worth checking out!! Pay for them for goodness sake! 🙂

[Hat tip: Matthew Wright–my good friend, and one of Ghrist’s grad students]

The Math of Roller Coasters

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Reposted from Wired.com:

Designing a good roller-coaster loop is a balancing act. The coaster will naturally slow down as it rises, so it has to enter the loop fast enough to make it up and over the top. The curving track creates a centripetal force, causing the cars to accelerate toward the center of the loop, while momentum sweeps them forward. Loose objects like riders are pinned safely to their seats. The acceleration gives the ride its visceral thrill, but it also puts stress on the fragile human body—and the greater the velocity, the greater the centripetal acceleration.

Coney Island’s Flip-Flap Railway, built in 1895, reached a neck-snapping 12 times the force of gravity at the bottom of its loop—more than enough to induce what pilots call G-LOC, or gravity-induced loss of consciousness. In other words, riders often passed out. In fact, any vehicle trying to get around a perfectly circular loop has to hit at least 6 g’s—enough to render most people unconscious.

To solve the problem, modern designers adopted an upside-down teardrop shape called a clothoid, in which the track curves more sharply up top than at the bottom. Then most of the turn happens at the peak, when the coaster is moving the slowest and the acceleration is least. Result: no G-LOC, just screams. The formula that helped them do it? ac = v2⁄ r.

Math ML

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On October 21, W3C (the governing body responsible for web standards) recommended a new version of its Mathematical Markup Language for use on the web. Here’s an article about it from ComputerWorld:

The W3C has updated its MathML standard for rendering mathematical notation on Web pages to better portray basic math symbols, as well as render mathematic symbols in more languages.

The World Wide Consortium (W3C) is hoping that this new version of MathML will be rolled into the other group of standards being incorporated in browsers with the HTML5 Web page markup specification, such as CSS (Cascading Style Sheets) and SVG (Scalable Vector Graphics).

The new standard represents basic symbols such as for multiplication, long division, subtraction, and the carries and borrows addition symbols.

The new markup will allow educational Web page designers to add these symbols onto the pages instead of going through the cumbersome process of embedding small images of the symbols or formulas into the pages. The symbols will also help assistive technology such as screen readers interpret the mathematical material.

more…

Before seeing this, I didn’t even realize such a thing existed. I read through some of the standards (here) and I wasn’t too impressed. For instance, check out this convoluted tagging that must be used to render the quadratic formula.

<mrow>
  <mi>x</mi>
  <mo>=</mo>
  <mfrac>
    <mrow>
      <mrow>
        <mo>-</mo>
        <mi>b</mi>
      </mrow>
      <mo>±<!--PLUS-MINUS SIGN--></mo>
      <msqrt>
        <mrow>
          <msup>
            <mi>b</mi>
            <mn>2</mn>
          </msup>
          <mo>-</mo>
          <mrow>
            <mn>4</mn>
            <mo>⁢<!--INVISIBLE TIMES--></mo>
            <mi>a</mi>
            <mo>⁢<!--INVISIBLE TIMES--></mo>
            <mi>c</mi>
          </mrow>
        </mrow>
      </msqrt>
    </mrow>
    <mrow>
      <mn>2</mn>
      <mo>⁢<!--INVISIBLE TIMES--></mo>
      <mi>a</mi>
    </mrow>
  </mfrac>
</mrow>

Contrast that to \LaTeX, which allows you to render it with this very simple code:

x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}

Ah…so nice! And here’s how it looks:

x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}

I’m open to having my mind changed–but I’m not seeing this new W3C recommendation as a usable standard. Anyone else have experience with it?

 

[Hat tip: Tim Chase, my beloved brother]

 

 

Benoit Mandelbrot

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I know this is old news, but I wanted to make sure and acknowledge that mathematical great, Benoit Mandelbrot passed away twelve days ago on October 14. There’s a nice set of videos on the TED blog if you care to check them out, including this TED talk that Benoit just gave in February of this past year:

At some point I’ll have to post more about fractals, for my own sake. I’d like to research them a bit more and make some of my own. For some beautiful fractals that appear in nature, you can see this post.