# What's New in Autograph 5

Thursday, 17 October 2019

## Contents

###### BACK TO TOP

## 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 a
_{1}x⁴+ a_{2}x³+ a_{3}x²+ a_{4}x + a_{5}c => should be a_{4}x⁴, a_{3}x³, a_{2}x², a_{1}x, a_{0}c - 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

###### BACK TO TOP

## 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

###### BACK TO TOP

## 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”:
- Data is first sorted in ascending order and numbered 1 to n
- The mean and SD of the dataset are calculated
- 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

###### BACK TO TOP

## 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