Difference between revisions of "Tutorial:Combining Spreadsheet View & Graphics View"

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|4||[[Image:Tool Show Hide Label.gif]]||Show the labels of both points in the [[Graphics View]].
 
|4||[[Image:Tool Show Hide Label.gif]]||Show the labels of both points in the [[Graphics View]].
 
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|-
|5||[[Image:Tool_Move.gif‎]]||Relative copy the inserted point coordinates to other cells in
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|5||[[Image:Tool_Move.gif‎]]||Relative copy the inserted point coordinates to other cells in column A:  
column A:  
 
 
# Highlight both cells A1 and A2 by using the mouse.
 
# Highlight both cells A1 and A2 by using the mouse.
 
# Click on the little square at the lower right corner of the highlighted cell range.
 
# Click on the little square at the lower right corner of the highlighted cell range.

Revision as of 18:42, 5 March 2012

GeoGebra provides different views of mathematical objects: a Graphics View, a numeric Algebra View and a Spreadsheet View. Thereby, all representations of the same object are linked dynamically and adapt automatically to changes made to any of the representations, no matter how they were initially created.

Spreadsheet Cells Input

In GeoGebra’s Spreadsheet View every cell has a specific name that allows you to directly address each cell. For example, the cell in column A and row 1 is named A1.

Note: These cell names can be used in expressions and commands in order to address the content of the corresponding cell.

You can not only use numbers in spreadsheet cells, but all types of mathematical objects that are supported by GeoGebra (e.g., coordinates of points, functions, lines). If possible, GeoGebra immediately displays the graphical representation of the object you enter into a spreadsheet cell in the Graphics View as well. Thereby, the name of the object matches the name of the spreadsheet cell used to initially create it (e.g., A5, C1). {{note|By default, spreadsheet objects are classified as auxiliary objects in the Algebra View. You can show or hide these auxiliary objects by selecting Auxiliary Objects from the styling bar at the top of the Algebra View.

Record to Spreadsheet

Preparations

  • Open a new GeoGebra window.
  • Go to Perspectives – Spreadsheet & Graphics.

Construction Steps

1 Tool Slider.gif Create a slider a with default interval and increment 1.
Note Hint: Select tool Slider and click in the Graphics View to set the position for the slider. In the appearing dialog window change the increment to 1 and click the Apply button.
2 Create point A by entering A = (a, 2a) into the Input Bar.
Note Hint: The value of slider a determines the x-coordinate of point A while the y-coordinate is a multiple of this value.
3 Tool Show Hide Label.gif Show the label of point A in the Graphics View.
4 Tool Move.gif Change the value of slider a to examine different positions of point A.
5 Tool Move Graphics View.gifTool Zoom In.gifTool Zoom Out.gif Use tools Move Graphics View, as well as Zoom In and Zoom Out to adjust the visible part of the Graphics View and make point A visible in all positions.
6 Tool Record to Spreadsheet.gif Record the coordinates for different positions of point A to the spreadsheet:
  1. Select tool Record to Spreadsheet. Then, click on point A in order to highlight it.
    Note: The coordinates for the actual position of point A are immediately entered into cells A1 (x-coordinate) and B1 (y-coordinate) of the spreadsheet.
  2. Now, change the value of slider a in order to record the coordinates of all other possible positions of point A to the spreadsheet as well.
    Note: Do not switch to another tool before moving the slider.

Relative Copy and Linear Equations

Preparations

  • Open a new GeoGebra window.
  • Go to Perspectives – Spreadsheet & Graphics.

Construction Steps

1 Tool Move Graphics View.gif Activate tool Move Graphics View and drag the origin of the coordinate system close to the lower left corner of the Graphics View.
2 In the Spreadsheet View, click on cell A1 enter the point coordinates (0, 0).
3 In the Spreadsheet View, click on cell A2 enter the point coordinates (1, 1).
4 Tool Show Hide Label.gif Show the labels of both points in the Graphics View.
5 Tool Move.gif Relative copy the inserted point coordinates to other cells in column A:
  1. Highlight both cells A1 and A2 by using the mouse.
  2. Click on the little square at the lower right corner of the highlighted cell range.
  3. Hold the mouse button down and drag the pointer down to cell A11.
6 Tool Move Graphics View.gifTool Zoom In.gifTool Zoom Out.gif Use tools Move Graphics View, as well as Zoom In and Zoom Out to adjust the visible part of the Graphics View and make point A visible in all positions.

Task 1: Examine the coordinates of the point sequence

What sequence of numbers is created if you apply the ‘relative copy’ feature of the GeoGebra spreadsheet the way it is described above?

Note Hint: Examine the x-coordinates of all created points and come up with a conjecture about how they are related. Then, check your conjecture using the ycoordinates of the points.


Task 2: Find the matching equation

Make a prediction about an equation that would create a graph going through all points of this sequence. Enter this equation into the Input bar in order to check your prediction.

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