Tag: math

Graphing Polynomials

Try it. You can change the order and coefficients of the polynomial. The default is the second order polynomial: y = x2.

I originally started putting together this interactive polynomial app to use in demonstrating numerical integration, however it’s a quite useful thing on its own. In fact, I’ve finally figured out how to do iframes, which means that the app is embeddable, so you can use it directly off the Muddle (if you want to put it on your own website you can get the embed code).

This app is a rewritten version of the parabola code, but it uses kineticjs instead of just HTML5 canvases. As a result, it should be much easier to adapt to make it touch/mouse interactive.

Working with Climate Data

Monthly climatic data from the Eads Bridge, from 1893 to the 1960’s. It’s a comma separated file (.csv) that can be imported into pretty much any spreadsheet program.

135045.csv

The last three columns are mean (MMNT), minimum (MNMT), and maximum (MXMT) monthly temperature data, which are good candidates for analysis by pre-calculus students who are studying sinusoidal functions. For an extra challenge, students can also try analyzing the total monthly precipitation patterns (TPCP). The precipitation pattern is not nearly as nice a sinusoidal function as the temperature.

Students should try to deconstruct the curve into component functions to see the annual cycles and any longer term patterns. This type of work would also be a precursor the the mathematics of Fourier analysis.

This data comes from the National Climatic Data Center (NCDC) website.

Rates of change: 4 cm/liter

The first stage rocket booster separates. Image from NASA via Wikipedia.

Fully loaded, the first stage of the Saturn V rockets that launched the Apollo missions would burn through a liter of fuel for every four centimeters it moved. That’s 5 inches/gallon, which, for comparison, is a lot less than your modern automobile that typically gets over 20 miles/gallon.

Ski Trip (to Hidden Valley)

Approaching a change in slope.

We took a school trip to the ski slopes in Hidden Valley. It was the interim, and it was a day dedicated to taking a break. However, it would have been a great place to talk about gradients, changes in slopes, and first and second differentials. The physics of mass, acceleration, and friction would have been interesting topics as well.

Calculus student about to take the second differential.

This year has been cooler than last year, but they’ve still struggled a bit to keep snow on the slopes. They make the snow on colder nights, and hope it lasts during the warmer spells. The thermodynamics of ice formation would fit in nicely into physics and discussion of weather, while the impact of a warming climate on the economy is a topic we’ve broached in environmental science already.

The blue cannon launches water into the air, where, if it’s cold enough, it crystallizes into artificial snow. The water is pumped up from a lake at the bottom of the ski slopes.

Influence Explorer: Data on Campaign Contributions by Politician and by Major Contributors

Influence Explorer is an excellent resource for assessing data about money in politics.

The website Influence Explorer has a lot of easily accessible data about the contributions of companies and prominent people to lawmakers. As a resource for civics research it’s really nice, but the time series data also makes it a useful resource for math; algebra and pre-calculus, in particular.

Wiggle Matching: Sorting out the Global Warming Curve

To figure out if the climate is actually warming we need to extract from the global temperature curve all the wiggles caused by other things, like volcanic eruptions and El Nino/La Nina events. The resulting trend is quite striking.

I’m teaching pre-Calculus using a graphical approach, and my students’ latest project is to model the trends in the rising carbon dioxide record in a similar way. They’re matching curves (exponential, parabolic, sinusoidal) to the data and subtracting them till they get down to the background noise.

Carbon dioxide concentration (ppm) measured at the Mona Loa observatory in Hawaii shows exponential growth and a periodic annual variation.

Regression with Gnumeric

A test regression (linear equation) using Gnumeric.

Finally, I’ve found a spreadsheet application (Gnumeric) with a reliable Solver for doing regressions. And it’s free. The only tricky part is that there’s no native port for Macs; you have to use a command line package manager to install it (I used Fink).

Gnumeric, however, seems to be an excellent tool for data analysis.