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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

1. Click
2. Select  and press
3. I will now put in the values for the triangle term# in List 1 and the number of dots in List 2.
1. Then click  again and select
2. Select  and press
3. Press  and then  selecting  and then.
4. On pressing  We will see the following screen:
1. Substitute with .

Middle

Texas Instruments-84 Silver Edition

1) Click

1. Select  and press
2. I will now put in the values of  in List 1 and values of  in List 2.
1. Then click  again and select
2. Select  and press
3. Press  and then  selecting  and then.
4. On pressing  We will see the following screen:
1. 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

1. Click
2. Select  and press
3. I will now put in the values of  in List 1 and values of  in List 2.
1. Then click  again and select
2. 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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