- Level: International Baccalaureate
- Subject: Maths
- Word count: 994
IB Math SL Portfolio Stellar Numbers
Extracts from this document...
Introduction
IB Mathematics SL
Math Portfolio
(Type I)
Stellar Numbers
Candidate Name: Ishaan Khanna
Candidate Session Number: 002603-011
Session: May 2012
The Doon School
The diagrams below show a triangular arrangement of evenly space dots in the format 1, 3, 6 onwards.
Completing the triangular numbers with three more terms (21, 28 and 36):
21 | 28 | 36 |
From the diagrams above, I can analyse the following data table:
Triangle term# | Number of dots |
1 | 1 |
2 | 3 |
3 | 6 |
4 | 10 |
5 | 15 |
6 | 21 |
7 | 28 |
8 | 36 |
Iwill now attempt to use quadratic regression to find out the general statement of the Triangular number .
Calculator used: Texas Instruments-84 Silver Edition
- Click
- Select and press
- I will now put in the values for the triangle term# in List 1 and the number of dots in List 2.
- Then click again and select
- Select and press
- Press and then selecting and then.
- On pressing We will see the following screen:
- Substitute with .
Middle
1) Click
- Select and press
- I will now put in the values of in List 1 and values of in List 2.
- Then click again and select
- Select and press
- Press and then selecting and then.
- On pressing We will see the following screen:
- Substitute with and with
General Statement:
Expression for the 6 stellar number at stage, from the equation above:
At stage:
Now the same for 5 and 7 Stellar shapes.
5 Stellar Shapes
S1 | S2 | S3 |
S4 | S5 |
Numerical form:
1 | 1 |
2 | 11 |
3 | 31 |
4 | 61 |
5 | 101 |
Calculator used: Texas Instruments-84 Silver Edition
- Click
- Select and press
- I will now put in the values of in List 1 and values of in List 2.
- Then click again and select
- Select and press
Conclusion
The general statement is derived from the expressions formed in the cases of a 5, 6 and 7 stellar numbers. From there I understood that the numerical parts in each equation can be substituted with the stellar number itself hence finding the general statement, in terms of p and n that generates the sequence of p-stellar numbers for any value of p at stage Sn.
Bibliography
TI-84 Quadratic Regression method learnt from:
http://fym.la.asu.edu/~tturner/MAT_117_online/Regression/Linear%20Regression%20Using%20the%20TI-83%20Calculator.htm
[Accessed on 21 February 2011]
Technology used:
Texas Instruments 84 Silver Edition calculator for Quadratic Regression
Microsoft Office 2010 & Microsoft Paint (Version 6.1) for shapes and figures
MathType (Version 6.7)
This student written piece of work is one of many that can be found in our International Baccalaureate Maths section.
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