Chaos and a War Against Set Theory?

This is Eddie, at the Friends Cafe at Monrovia, CA, enjoying lunch and a great Friday.

Chaos

Below are three pages from a beautiful book, "An Eye For Fractals" by Michael McGuire (1991). I got this from Book Alley in Pasadena, CA. Book Alley has every book ever written, or at least it felt like it when the aisles literally full with books.

My understanding of chaos theory and fractals is limited at this point. Making fractals involve applying repeating operations or calculations a lot (and yes this can include an infinite) of times and evaluating the results. Famous examples of fractals include the Koch Snowflake, Sierpniski Triangle (the TI-82 manual had a program to generate this), the Cantor Set, and the Barnsley Fern.

I have tried to plot the Madelbrot Set on a TI-84+, unsuccessfully.

Set Theory Is Evil!

Or this is what the publishers at the Christian publisher A Beka want us to think. I first heard of the publisher while I listening to episode #108 of Math/Maths Podcast. Clicking this sentence takes you to the Math/Maths podcast page. You can also download their podcast through iTunes.

They referred us to an article written by Maggie Koerth-Baker, which you can read by clicking here.

I agree with Koerth-Barker. The fundamentalist books are out of touch with reality and is a disguised as an attack on anyone and everyone who does not belong to the fundamentalist tribe. To exclude or twist facts to fit an ancient text and to teach it to children can pry the door to another Dark Age.

Mathematically, without set theory, we would be without, among other things, we would be without the ability to qualitatively compare groups of items, vector spaces, computing, and how to order objects of set. I would think that with A Beka's objection, we would not be able to tell which one of two members is greater or less - which would really screw up subtraction and the number line. However, while I was writing this blog entry, I was informed by Samuel Hansen (of the Math/Maths podcast) Twitter that their objection is to modern set - so ordering of numbers and basic math is OK. Thanks, Samuel.



Eddie


This blog is property of Edward Shore. © 2012

Programs for HP 48S and What's Coming Up

HP 48: Law of Sines and Cosines, Quadratic Formula, and Cubic Formula.

Hi everyone! Recently, a poster on the MoHPC HP Calculator Forum asked for programs for solving triangles and finding roots for polynomials. (link here)

I will repost the programs here. They have been done with the HP 48S.

Law of Sines:

sin(θ1)/S1 = sin(θ2)/S2. Apply this to any of the two sides and their corresponding angels.

θ which can be typed by pressing:
HP 48S: [alpha] [right shift] (F)
HP 48G: [alpha] [right shift] (F)
HP 50g: [alpha] [right shift] (T)

LAWSIN:

<< 'SIN(θ1)/S1=SIN(θ2)/S2' STEQ 30 MENU>>

Law of Cosines:

A^2=B^2+C^2-2BC cos θ

LAWCOS:

<< 'SQ(A)=SQ(B)+SQ(C)-2*B*C*COS(θ)' STEQ 30 MENU>>

30 MENU brings up the calculator's solver using whatever is stored in STEQ.

QD: (Quadratic Formula) - Credit goes to the document "1 Minute Marvels" by Wldoek Mier-Jedrzejowicz and Richard Nelson (They have this program named 'quad')

Input:

3: A
2: B
1: C

Output:

2: root 1
1: root 2

<< 3 PICK / SWAP ROT -2 * / DUP SQ ROT - √ + LASTARG - >>

SQRT: Square Root

CU: Cubic Formula Uses the program QD above. This program finds the roots of AX^3+BX^2+CX+D=0

Input:
4: A
3: B
2: C
1: D

Output:
3: root 1
2: root 2
1: root 1

Program:

<< → A B C D
<<
C 3 A * / B SQ 9 A SQ * / - 'Q' STO
C B * A SQ / 3 D * A / - 6 / B 3 ^ 27 A 3 ^ * / - 'R' STO
R Q 3 ^ R SQ + √ + 3 XROOT 'S' STO
R Q 3 ^ R SQ + √ - 3 XROOT 'T' STO
S T + B 3 A * / - 'X' STO
X
B A X * +
C B X * + A X SQ * +
QD
{Q,R,S,T,X} PURGE >> >>

What is Coming Up

Coming in August, I will do a short series which I will use a graphing calculator with programming capabilities, most likely the TI-84 Plus, to demonstrate how programming is used to assist in mathematical applications: including finding the amount of miles between two places, projectile motion, and random walks.

If you get a chance, check out the Math/Maths Podcast. Link: Pulse Project

Until then,

Eddie


This blog is property of Edward Shore. © 2012