GeoGebra

GeoGebraMathematics Cookies

Term 2 Sabbatical

Hwa Chong Institution

*What is GeoGebra?

*a free interactive geometry software*started the in 2001 by Markus Hohenwarter at the

University of Salzburg

*Why use GeoGebra?

*user friendly & convenient*few system requirements (only requires Java)*new online or WebStart version does not need

installation*when doing your project GC design on the 4th day

you can use it to graph your draft out either the equations or the shapes then retrieve the equations first

*How to get GeoGebra?

*Use it online (Online Version):*http://www.geogebra.org/webstart/geogebra.html

*Use the applet downloaded directly from internet (WebStart Version)*http://www.geogebra.org/webstart/geogebra.jnlp

*Download and install it onto your computer (Installer Version)*http://www.geogebra.org/cms/en/installers

*Download it onto your thumbdrive (Portable Version):*http://www.geogebra.org/cms/en/portable

*HOW TO USE GEOGEBRA?

*Components of GeoGebra

Toolbar

Input bar for equations

Algebra View Spreadsheet View(Not often used)

Chart View

*Algebra View

*Lists all objects there are on the chart*Free objects – User defined functions (e.g. linear

functions)*Dependent objects – Objects drawn with reference to

free objects (e.g. quadrilateral plotted from 4 user-defined points)*Auxiliary objects – Objects classified by the user as

auxiliary (no specific use)

*Chart View

*Shows the chart & its objects*To change the properties of a function or shape, right

click on them*Polar coordinates – change the object from

Cartesian to Polar*Trace to Spreadsheet – records the x & y values

of the object into the spreadsheet view*Auxiliary Object – classify the object as auxiliary*Copy to Input Bar – copy the formula of the

object to the input bar*Object Properties – format the object

*Functions commonly used & their equations

*Line: y=mx+c*Quadratic: y=ax2+bx+c or y=a(x-h)2+k (derived

from completing the square)*Cubic: y=px3+qx2+rx+c*Circle/Eclipse: (x-a)2+(y-b)2=r2

*where r is radius of circle & the centre’s coordinates are (a,b)

*Trigonometry: y=sin(x), y=cos(x), y=tan(x)*You can also input other equations (need not be

y=something), but for Graphical Calculators remember to make y the subject

*Inputing functions into GeoGebra

*Functions involving x*func(x)*x surrounded by round brackets* func is the short function name, common ones are:* sine – sin(x)* tangent – tan(x)* cosine – cos(x)* square root – sqrt(x)* cube root – cbrt(x)* absolute value – abs(x)* natural logarithm - ln(x)* common logarithm – lg(x)

*Other functions*input as normal with exceptions

* powers (x to the power of y) – x^y

*Setting domains in GeoGebra

*A limitation in GeoGebra is that domains are hard to set*Domains are used if you only want a function to be

visible at a certain range (of x or y values)*e.g. a line y=0 drawn from x=0 to x=5 has a domain of

x<=5 & x>=0*There are many methods tried out using IF Loops*GeoGebra IF Loop: If[<Condition>,<Statement if

true>,< Optional Statement if false>]*However, the main objective of GeoGebra in this

sabbatical is to design the draft of the GC design, so the domain can be ignored as it can be set later in the Graphic Calculator.

*EXAMPLEOlympic Logo

Theme: YOG

*Step 1

*We only want to use the positive values for x & y. Move the drawing pad so that only the positive region of the graph can be seen.

click on this

then drag to this positive region

*Step 2

*Draw a circle*Click on circle tool*Select middle point then hover the cursor away from it to

set the radius of the circle

click on thisselect the middle point

then hover the cursor here to set radius

*Step 3

*Repeat the process for the other 4 rings*Copy the generated equation in the algebra view into

the input bar & create an identical circle*Use the move tool to move the circle (click on the

circle’s perimeter)

rightclickhere

then click here…

and the equation is here

*Step 3 continued

*Repeat the process for the other 4 rings*Generate the other 4 circles*Resize where appropriate depending your preferred

range of x & y values

To select a circle from 2 identical circles you either:• click the circles and choose

the one you want to select; or

• hide one of the circles in Algebra View, then drag the visible one out

*The EndAny Questions?

Help & Support: http://www.geogebra.org/cms/en/help