Introduce Autograph

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

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

please download sample files for the workshop here > http://web.hku.hk/~amslee/autograph.zip

Graph Paper Format choose graph paper format or show subdivisions

On-screen Keyboard

Slow Plot and Control

Constant Controller

Insert Image

Some readings about use of images and videos with dynamic tools From

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

Oldknow, A. (2003) Mathematics from still and video images

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

Micromath (Summer, 2003, pp.30-34)

Vidshell

http://www.atm.org.uk/mt/micromath/mm192oldknowa.pdf Oldknow, A. (2003) ICT - bringing maths to life and vice versa Micromath; Summer 2003; 21, 2; Academic Research Library. pg. 16

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

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

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

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

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

with the original graph hidden, discuss about the nature of the critical points

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

Derivative and Tangent

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

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

Derivative and Tangent

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

Best fit to Data 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.

Matrix create 4 points, group them to make a shape

select the shape and make a matrix transformation

Matrix drag the original shape enter the matrix

the image is shown

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

a point on the normal through the origin

equation

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