introduce Autograph
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Transcript of 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