What's New in Autograph 5

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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

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

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’

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 =

Angle from two points

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

Ray from two points

• Right click > Line > Ray

Quadratic from three points

• x=f(y) option

Unit gradient triangle from point on graph

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

New transformations

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

Regression Lines

• y-on-x & x-on-y
• Show dotted < x_min and > x_max

New intersection icon

• Equivalent to pressing CTRL to find intersections, max, min

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

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.

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)

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

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)

Arc Length from two points on graph

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

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)

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))

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 parametric plotting improved

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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.

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.

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.

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'

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