Sequences in GeoGebra
Sequence commands are entered in the input field. Watch spacing and brackets carefully!
Spaces always follow commas, and a space in an expression represents multiplication!
To Create:
Basic Commands
List of objects:
Sequence[expression e, variable i, number a, number b]
Default step size = 1
Or
List of objects:
Sequence[expression e, variable i, number a, number b, step size]
nth Element in a list:
Element[List L, number n]
Length of a list:
Length[List L]
Minimum:
Maximum:
Min[List L]
Max[List L]
Activity 1: Create a List of Objects (Points): See file: seq_line1.ggb
Open GeoGebra
View: Algebra Window, Axes, and Grid--Option:
Point capturing (on grid)
In input field, enter the following points:
A=(0,1)
B=(1,4)
C=(2,7)
D=(3,10)
E=(4,13)
Zoom out, move drawing pad to see 1st Quadrant.
Create a line through Point A and Point E.
In algebra window, under dependent object, select
line a. Control click. Select y = a x + b.
Hide line a.
In input field, enter Sequence[(k, 3 k+1), k, 0, 15]
To place more points on the line: Left click in the input field. Page Up Arrow.
Change entry to: Sequence[(k, 3 k+1), k, 0, 15, 0.5]
What happened? Change step size to 0.1. What happened?
Sequences in GeoGebra
MSP Summer Institute 2007
Joan Carter
Activity 2: Find the nth term in a Sequence: See file: seq_line2.ggb
Create a list of points: Sequence[(k, 3 k+1), k, 1, 15]
Find the 4th term: Element[L1,4] . Point A is created at (4,13), so the 4th term is 13.
Find the 7th term: Element[L1,7] . Where is Point B? How about the 200th term?
Create a slider: Number, 0 - 300, increment = 10
Redefine list of points (Command click on L1): Sequence[(k, 3 k+1), k, 1, n]
Element[L1, n]
Set slider to n = 200. What’s the 200th term? (Look in the algebra window.)
Activity 3: Line Art (Approximation of Bezier’s curve):
See file: seq_line_art1.ggb
For Sequences of Points:
Create a list of points on the x-axis from 1 to 10: Sequence[(k,0), k, 1, 10]
Create a list of points on the y-axis from 10 to 1: Sequence[(0,k), k, 10, 1, -1]
For a Sequence of Segments, join the first position of L1 with first position of L2; that’s
(1, 0) with (0, 10). We are using nested commands here. Be careful with brackets!
Sequence[Segment[Element[L1,k], Element[L2,k]], k, 1, 10]
Activity 4: Line Art Tool: See file: seq_line_art2.ggb.
Activity 5: Points and Segments on a Circle:
See file: seq_circle_segments1.ggb
Point A
Slider n, number, 2-20, increment 1
To list points: Sequence[ Rotate[A, i * 360 / n ], i, 0, n-1]
To list segments: Sequence[Segment[Element[L1,1],Element[L1,i]], i, 2, n]
Activity 6: Advanced Segments on a Circle and Rosettes:
See files: seq_circle_segments2.ggb and seq_circle_segments3.ggb
Sequences in GeoGebra
MSP Summer Institute 2007
Joan Carter
Line Art Approximation of Bezier’s Curve
Starting point: Connect
Sequences in GeoGebra
with line segment.
MSP Summer Institute 2007
Joan Carter