What's New in Autograph 5

Thursday, 17 October 2019

Contents

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2D Page

'Label objects' setting in the Axes Menu

  • Clicking 'Label objects' — objects will be labelled from now on.
  • Clicking 'Label Points only' – this will not label other objects (lines, etc)
  • Any new 2D page opens with 'Label Objects' off
  • New right-click options on selected points, lines etc:
    • 'Show Labels'
    • 'Hide Labels'
    • 'Edit draw options' (e.g. in the case of points, change their shape)
  • New right-click options on single point:
    • 'Edit Label'
  • Note: Labels are important when using the CALCULATOR or XY ATTRIBUTE POINT as both refer to host objects by label
Labelling objects

Line Tests

  • Select two lines/rays/segments:
    • Parallel or perpendicular. If the lines or line segments are parallel, single arrows are placed at the mid-point (+ a bit). If lines are perpendicular a right-angle sign is placed at the intersection
  • Select two or more segments:
    • As above together with test for equality which is displayed as marks at mid-point
  • Select any line with ticks & ’Remove Line Tests’:
    • Deletes all test marks in this and associated lines
Line tests

Fixed length line from point

  • Right click > line > Fixed Length Line
    • Enter length (‘d’) of line. Autograph then draws and labels a line horizontally to the right, which can then swing round a circle of radius ‘d’
Fixed length line

Create rectangle from two points

  • With 2 points selected, right click and create > Rectangle. Enter height; plotted clockwise from the 2nd point
  • Attributes: side, height, Perimeter = 2 * (side + height), Area = side x height
  • Status bar: Rectangle a x b, Area =
Rectangle creation

Angle from two points

  • Right click > Create > Angle
    • Enter angle (‘θ’). Autograph then draws and labels an angle ('B'), option for 'clockwise'
Angle creation

Ray from two points

  • Right click > Line > Ray
Ray creation

Quadratic from three points

  • x=f(y) option
Quadratic from 3 points

Unit gradient triangle from point on graph

  • With point on graph selected Right click > Line > Unit Gradient
Unit gradient triangle

New transformations

  • Rotation, Enlargement, translation, etc
  • Clockwise option for rotation
Transformations

Regression Lines

  • y-on-x & x-on-y
  • Show dotted < xmin and > xmax
Regression line

New intersection icon

  • Equivalent to pressing CTRL to find intersections, max, min
New intersection icon

New click and hold options

  • With daya set drawn. Click-hold-drag as alternative to CTRL-drag to select/move points in a data set. For use on white-boards and touch interfaces
  • In select mode. Click (marquee select) and Hold (drag scene)
  • In zoom mode. Click-release: Zoom in/out, Click-drag: select zoom area
Move with click-and-hold

Points recorded as data

  • Create an “XY” attribute point from two objects (Here the two attributes are x-coordinate of the point on curve and the value of the slope of the gradient). Tick “Record to Results Box”
  • With ‘A’ selected click Animation and set the step to 0.25 Step along the curve, and note the values recorded in the Results Box.
Points recorded as data

Major revision of plotting procedures

  • Floor(x) and ceil(x) and int(x) now plot with no verticals
  • Plotting a discontinuity e.g. y = (x² − 4)/(x − 2)
  • 2D plotting revised and improved, e.g. y = sinx cos(1/x)
Floor(x) and ceil(x) and int(x) now plot with no verticals

Gradient function and polynomial best fit now behave like entered functions

  • So you are now able to enter point on curve, draw tangent, create area (2 pts); draw gradient function
  • Also Animation Controller available to animate order of polynomial
Gradient function now behaves like an entered function

New Area options

  • ‘General’ and ‘Mid-interval Rule’ added
  • ‘General’ is Simpson's Rule with 50 divisions and standard object fill
  • Rectangles (left) was (-) and Rectangles (right) was (+). “left” means the height used is the left of the interval, right for right of the interval.
  • Can calculate 'area between': Select 2 points (on or off graph) + TWO functions (in order)
New area options

Arc Length from two points on graph

  • With 2 points selected on a graph Right click > Arc Length, option to show centroid
Calculate arc length

Subscripts!

  • Enter using eg a_2 for a₂ in the range 0 … 9. Manage constants redesigned: subscripts for lower-case and uppercase constants (single upper-case constants not permitted)
Subscripts

Miscellaneous Small Changes

  • Can change 'UI theme' in preferences
  • New option “Accessibility” to adjust colours in preferences. Used for selection by those hard of sight, or selection not showing well on whiteboards.
  • Attributes of polynomials >3 renumbered: e.g. quartic is a1x⁴+ a2x³+ a3x²+ a4x + a5c => should be a4x⁴, a3x³, a2x², a1x, a0c
  • Text Box and Calculator: MathML converts to single-line notation when copying
  • Origin circle no longer gets too small if window size reduced
  • “Create data set from graph” does not have “Join Points” ticked
  • Image attached to a point: takes its gradient at the point, not the middle
  • With 2 points selected Right click > Point > Ratio is now the calculatd the other way round
  • Pallet of font colours has been extended
  • In start-up options: Manual limits can take constants
  • Polygons – allow (integer) constants for number of sides
  • 2-point Vector: text box says AB () instead of “Join Vector”
  • Can 'nudge' images with arrow keys (and Ctrl)
  • XY Data`: Column Headers ticked by default
  • Import and export data (2D and Stats): CSV or TAB options + saves heading(s)
  • 2D page: CTRL-MOUSE-WHEEL zoom speeded up
  • Default Animation parameters changed from 0 … 10 and step of 1 to –3 … 3 and step of 0.1
  • In Edit Axes, if the variables have been changed to 't' and 'v' in ranhes the options now say't' and 'v' not 'x' and 'y'
  • Accept two ‘ (prime symbol) as equivalent to “ (double prime symbol) when entering 2nd order differential equations
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3D Page

Arc Length and Surface of Revolution

  • With 2 points selected on a 2D graph Right click > Arc Length
  • Option to draw axis of revolution in the form y = k (plot as 2D)
  • With Arc length selected: Right click > Surface of revolution: enter axis of revolution (If not drawn and selected)
  • Arc length can be a line segment (must be in x-y plane, so z = 0))
Surface of revolution

The 3D “Create” Sub-menu

  • Parallelepiped
    • With 1 point and 3 vectors selected, right click > 'Create' > 'Parallelepiped'
    • Attributes: Volume = (a x b ) • c
  • Sphere
    • With 1 point selected, right click > 'Create' > 'Sphere' > enter radius
    • With 2 points selected, right click > 'Create' > 'Sphere' (center at first point)
    • Attributes: radius, surface area, volume
  • Cylinder
    • With 2 points selected, right click > 'Create' > 'Cylinder' > enter radius
    • Attributes: radius, height, surface area, top/bottom area
  • Cube
    • With 2 points selected on a plane, right click > 'Create' > 'Cube' (choice of positive or negative orientation and clockwise/anti rotation)
    • Attributes: Side length, Surface area, Volume, Inside/Outside radius
  • Tetahedron
    • With 2 points selected on a plane, right click > 'Create' > 'Tetrahedron' (choice of positive or negative orientation and clockwise/anti rotation)
    • Attributes: Side length, Height, Surface A, Volume, Inside/Outside radius
  • Polygon
    • With 2 points selected on a plane, right click > 'Create' > 'Regular polygon' > enter number of sides
    • With 3 points selected, right click > 'Create' > 'Polygon'
    • With ≥ 3 points selected on a plane, right click > 'Create' > 'Polygon'
    • Attributes: Sides, perimeter, area, centre, (Additionally if regular: side length, inside/outside radius, int angle)
  • Right pyramid
    • With 2 points selected on a plane, right click > 'Create' > 'Regular Pyramid' > enter number of sides and height
    • With 1 polygon selected on a plane or 1 plane side of a cube, tetrahedron, pyramid or prism selected, right click > 'Create' > 'Right Pyramid' > enter height
    • Attributes: Sides, side length, height, slant height, Surface area, volume, inside/outside radius, slant height, base area
  • Right prism
    • With 1 polygon selected on a plane or 1 plane side of a cube, tetrahedron, pyramid or prism selected, right click > 'Create' > 'Right Prism' > enter height
    • Attributes (regular pol): sides, height, Surface area, volume. base area, centre, side length, inside/outside radius
  • Cuboid
    • Enter and select 4 points on a plane in a rectangle, right click, 'Create' > 'Polygon'
    • With the polygon selected, right click, 'Create' > 'Right Prism' > (enter height)
    3D Shapes

3D parametric plotting improved

3D parametric plotting
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Statistics Page

Dynamic Raw Data

  • When entering Raw Data: Option to show the data as a Dynamic Dot Plot
  • Dynamic points in a dataset can be moved around holding CTRL and drag or HOLD and drag
  • Points can also be added in Point Mode (max 1000 points). Such points when selected (using marquee select) can add to an existing dataset or can create a new dataset. Subsequent dependent objects will adjust accordingly
  • A listed Raw Data set can be deselected to allow a new set of data points to be added.
  • Individually selected dynamic data point: coordinates given in status bar.
Move raw data points

Box and whisker plots

  • Outliers: Data points further out than 1.5 x IQR are shown as potential outliners. The Box Plot extreme verticals are the lowest and highest data that can be considered not to be outliers.
  • Can plot multiple box plots. Must be entered one at a time, but individually labelled. Autoscaling optimised, and each on has a LABEL based on the individual data column header. Label can be edited using the right-click option with the parent box plot selected.
Box plots

New Statistics Object: Q-Q Normal Plot

  • A test for normality used in Core Maths on a raw data set. So with a raw data set entered, right click option “Q-Q Normal Plot”:
    1. Data is first sorted in ascending order and numbered 1 to n
    2. The mean and SD of the dataset are calculated
    3. The dataset is formed of three columns: Data, Number i (i... n), Quantile Normal
  • Normal Quantiles are plotted against the data on equal scales. The line y = x is drawn dotted
  • Select the Q-Q plot and right click > 'Table of Statistics' to show 3 columns in the Results Box.
Q-Q normal plot

Misc

  • Minor fix to the Statistics page: Normal areas plotted nicely
  • Objects can now be arranged in ORDER
  • Can add image
  • Variance now uses /(n-1) form throughout
  • Vertical scaling and its label are determined by the first object plotted
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Complex Number Page

New object: Circle

  • Right click on complex number page > 'Circle' > input radius

New creations

  • With one complex number selected you can now create a vertical line, horizontal line and circle from single complex number
  • With two complex numbers selected you can now create a straight line, line segment, perp. bisector and ellipse (enter sum of radii)
  • With three complex numbers selected you can now create a circle and an ellipse (1st 2 CNs are the foci, then point on the ellipse)

New Complex transformations

  • for lines, circles and ellipse, and a single point

Loci!

  • With a single point and its complex transformation selected, right click > 'Locus'
Complex transformation loci

Show/hide vector to origin

  • With single point selected, right click > 'Edit complex number' > Uncheck 'Show Vector to Origin'

Calculations on complex numbers

  • Including: 'Multiply by Scalar', 'Raise to Power', "Multiply by i', 'Complex Conjugate', 'Real Part', 'Imaginary Part', 'nth Roots'
  • Labels are automatically added

Axes Auto scaling

  • Always includes origin
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Miscellaneous

Revised level selector on start-up

New level selection on load

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