Monthly Archives: March 2012

Autograph: (1.2, 3.4) or (1,2; 3,4) ?

Many countries, eg England, use Decimal  = ‘.‘ and List Separator = ‘,‘  ie (1.2, 3.4)
Others, eg France, use Decimal = ‘,‘ and List Separator = ‘;‘  ie (1,2; 3,4)

The computer must use the same for ALL applications so that, for example, both Excel and Autograph are expecting the same convention.  Additionally Autograph uses the List Separator to enter Parametric Equations, eg x = sint, y = cost.

Apple and Windows computers treat this topic a little differently.
Download this Word doc that summarises the situation:

Decimal Symbol and List Separator

Decimal Symbol and List Separator

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Autograph: onscreen keyboard

The onscreen keyboard allows Autograph users to input one-line mathematical expressions using a wide variety of symbols that are coorrectly interpreted, eg
   sin²2θ, 2x−3y≤6, −b±√(b²−4ac), y=|x|
It is also invaluable when using a whiteboard or a walk-about tablet.
This short video explains

Image

Autograph: saving favourite axes settings

Autograph: saving axes settings

It is a common request to be able to save axes settings within Autograph. The problem is where would they be stored? You would neeed a personalised preference section, not too difficult for a single user, but tricky to manage in a networked environment.

The simple answer is to save a particular Autograph page with the axes just so, then load that file when needed.  This short video explains.

Autograph: Matrices and Transformations (2D)

This video summarises the effect of a matrix transformation on different object types: the unit square, the graph of y = x², and a flag. In each case there is a variable parameter included so that animations can be set up.

Download associated Autograph file
3×3 Matrix transformations are also available on a 3D Autograph page.

Autograph: The derivative of y = sin2x and the Chain Rule

This video explores the slope of a tangent on y = sin2x at x = a
and the slope of the tangent on y = sinx at x = 2a.
The Chain Rule suggests that if y = sin2x then dy/dx = 2cos2x,
so at x = a, dy/dx = 2cos2a
For the ‘parent’ function y = sinx, dy/dx = cosx,
so at x = 2a, dy/dx = cos2a, a half of the above.

Download associated Autograph file

Autograph: magnitude and direction of a vector

An Autograph tip to display the magnitude and direction of a vector [r, θ] that is otherwise displayed only in cartesian coordinates [x. y].

Download associated Autograph file