Some uses of MATHEMATICA in Don’s teaching

The latest one: Rotating a sine wave 60 degrees ccw.

1. Go to A Map to Calculus , click on “Iteration or Feedback” (upper left), and see the patterns Maura finds.

2. Go to A Map to Calculus , at lower right , click on “Find the Sqrt 40 by averaging and iterating”

3. Don and three of his students found the Dottie number, at http://www.mathman.biz/html/Dottie_Number.html ).

4. Have Mathematica graph 2 iterations of y=5-6/x (an infinite continued fraction, from solving the quadratic equation x2-5x+6=0, whose roots are {2,3}). Where do the curves intersect and what kind of curve is each one?

5. Anae plotted (2+i)n for n = whole numbers, without Mathematica, then Don plotted (1+i)n where n is a whole number, using Mathematica to get a spiral. He then wrote the coordinates in complex number form, eix form and cis form. Click on (1+i)n  spiral” on Don’s  A Map to Calculus (at the bottom) . Three spirals were then plotted using Mathematica, with the following commands:

ParametricPlot[{Re[(1+ ä)^n],Im[(1+ ä)^n]},{n,0,12}]

ParametricPlot[{Re[(()^n)*ã^(ä*n*p/4)],

Im[(( )^n)*ã^( ä *n*p/4)]},{n,0,12}]

ParametricPlot[{Re[(()^n)*(Cos[n* p /4]+ ä*Sin[n* p /4])],

Im[(()^n)*(Cos[n* p /4]+ ä*Sin[n* p /4])]},{n,0,12}]

See IES applet based on Don’s i^i , in chapter 11, linked on that page and they get fractals!

7. Using Mathematica as one of 3 ways to find, and click on “the vol of a pyramid/Vol of a cube (with the same base)” on Don’s A Map to Calculus

8. Using Mathematica to make a list of the first 30 Fibonacci numbers.

10. Don uses Mathematica to make a polar graph of r = 2, a spiral, then sees if 90º segments are similar shapes using “the eye test”. Click on spirals r = 2t  on Don’s  A Map to Calculus (left and below Graphs)

11. Don uses Mathematica to make a polar graph of the Nautilus Shell equation and compares it to a rubbing of the shell and the measurements his students make of the shell.

12. Ian uses Mathematica to graph the output of his rule which finds E using polypowers. Click on “Infinite Sequences” on Don’s  A Map to Calculus

13. Find, and graph, the three cube roots of 8. A good lead into de Moivre’s theorem.

14. Click on derivatives on Don’s  A Map to Calculus , go to Elizabeth asked Don..”.  He graphed a function, its first and second derivatives, and they compared the properties of each curve and the relationships between them. [Don later used this lesson to have a great 1 hour discussion of derivatives and integrals, with Jay, a HS senior. He was studying calculus with Don, even AP Calc test questions, at the culmination of 12 years as Don’s student! He has since graduated HS and will attend the U of Illinois in the fall of 2011].

15. David’s method gets a polynomial function for Don’s pairs of numbers, made much simpler with Mathematica.

16. Geoffrey uses Mathematica in his study of polypowers

17. Use of Mathematica in Ch.11 answers

18. His Dad worked with Geoffrey using Mathematica to do the infinite sum

19. Fractions to decimals by MaggieP

20. See

21. Don graphed 1/x in Mathematica and found the following: The area under the curve 1/x from 1 to 3 is equal to the loge 3 = ~ 1.0986 ...

22. Michael works on infinite series  Don showed Michael how to do this in Mathematica® and Derive. Michael tried things to show how his rule works for big numbers. ...

23. Patterns in graphs (#20).The graph of (1 + 1/n)^n by Geoffrey in Mathematica® approaches E

method #4

25. Introducing trigonometry to do rotations and rotation equations ...(I graphed the ellipse   in Mathematica, rotated it 90o CCW, then I copied them into my paint program where I..

26. Geometric Sequences and The Frequencies of the 88 Keys on a Piano The following graph (bottom of page) done in Mathematica, shows a polar graph of the frequencies for the octave from middle C 3 (261.63) to C4 (523.25).

27. Nanako comes from Japan to work with Don , June 16, 2008 ... Don showed Nanako and Mum how Mathematica can get 100 digits for The Golden Mean quickly: N[(Sqrt[5]+1)/2100] = ... (at the bottom of the page).

### 28.Don's work on Polypowerswith the help of Theo Gray

30.Tim finds a new way to write the nth term of an infinite geometric series

31. Moving a graph, write the equation.

33.