introduce Autograph

http://www.autograph-maths.com/

http://web.hku.hk/~amslee/auto.pdf

Graph Paper Format

choose graph paper format or show sub-divisions

On-screen Keyboard

Slow Plot and Control

Constant Controller

Insert Image

Some readings about use of images and videos with dynamic tools

Oldknow, A. (2003)ICT - bringing maths to life and vice versaMicromath; Summer 2003; 21, 2; Academic Research Library. pg. 16

Oldknow, A. (2003)Geometric and Algebraic Modelling with Dynamic Geometry SoftwareMicromath (Summer, 2003, pp.16-19)

http://cripe03.ugent.be/Vidshell/Vidshell.htm

Vidshell

http://www.atm.org.uk/mt/micromath/mm192oldknowa.pdf

Oldknow, A. (2003)Mathematics from still and video imagesMicromath (Summer, 2003, pp.30-34)

Sharp, B.D. (2007)Making the Most of Digital ImageryMathematics Teacher 100-9, May 2007, pp.590-593free preview at

http://nctm.org/publications/mt.aspx?id=8594

a free program for video analysis is mentioned in Oldknow (2003)

http://www.atm.org.uk/mt/micromath.htmlFrom

Inequalities

Derivative and Tangent

show derivative

when slow plot is turned on, tangent is shown as the derivative is traced

the trace stops at critical points and continues with the pause button

Derivative and Tangent

right click the original function and hide it

double click the original equation to edit it;

while the original graph is still hidden, the derivative graph is updated

Derivative and Tangent

use the point tool to add new points on the derivative graph, near the critical valueswith the original

graph hidden, discuss about the nature of the critical points

Derivative and Tangent

click one of the point on graph, use the up /down arrow to move it to the hidden graph at the corresponding x value

use the scribble tool to mark the sketch the graph around the critical point

Derivative and Tangent

the original graph is shown again, compared with the previous sketch

With a DATA SET and ANY y = f(x) graph with constants:

This will find (by least squares) the best value of the constants to fit the data, e.g. y = asin(bx + c) + d. Select the graph and use the option “Update Results Box” to obtain a list of the constants.

Best fit to Data

Matrix

create 4 points, group them to make a shape

select the shape and make a matrix transformation

Matrix

enter the matrix

the image is shown

drag the original shape

add base vectors; move the shape along the axes

a single sample of size 5 with mean 500 sample means, n=200

Probability Distribution

user defined probability distribution; dot plot and histogram from data generated

3D coordinates, vectors and surfaces

enter equation of plane or other surfaces

equation

a point on the normal through the origin

3D coordinates, vectors and surfaces

add points and vectors on the plane, create cross product

Solid of Revolution

turn to x-y orientation

enter equation of function, plot as 2D equation

click the curve and find area

Solid of Revolution

click the area and find volume

in slow plot mode, the solid generates gradually

number of division is adjusted in animation setting