• Join over 1.2 million students every month
• Accelerate your learning by 29%
• Unlimited access from just £6.99 per month

# 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.

## Found what you're looking for?

• Start learning 29% faster today
• 150,000+ documents available
• Just £6.99 a month

Not the one? Search for your essay title...
• Join over 1.2 million students every month
• Accelerate your learning by 29%
• Unlimited access from just £6.99 per month

# Related International Baccalaureate Maths essays

1. ## Math IB HL math portfolio type II. Deduce the formula Sn = ...

a1 + (n - 1)d We know: am = a1 + (m - 1)d ap = a1 + (p - 1)d aq = a1 + (q - 1)d am + an = ap + aq = a1 + (p - 1)d + a1 + (q - 1)d = 2a1 +

2. ## Extended Essay- Math

1/4 *ï¿½ï¿½ï¿½1ï¿½"}xï¿½Dï¿½?"ï¿½1ï¿½ï¿½ï¿½ï¿½Eï¿½...ï¿½ã¿±ï¿½qnmï¿½_ï¿½pï¿½ï¿½ï¿½<ï¿½aï¿½Uï¿½ï¿½ï¿½JÆ§ï¿½cï¿½-6Xï¿½qï¿½yï¿½-ï¿½ï¿½ï¿½#1/4 ï¿½{ï¿½ï¿½ï¿½XÙq}b% Yï¿½ZCAï¿½ï¿½n#ï¿½1ï¿½^3/4HGï¿½`dï¿½3%(tm)ï¿½ï¿½5ï¿½.(r)Mï¿½pï¿½9ï¿½ï¿½^!ï¿½0ï¿½Hfï¿½ï¿½ï¿½ï¿½ yï¿½`ï¿½S5ï¿½R^Rï¿½aï¿½Cï¿½ï¿½ï¿½ï¿½@Üï¿½1/4rï¿½T"ï¿½+j"ï¿½ï¿½b+Roï¿½dï¿½2Fï¿½3/4ï¿½<'g(tm)8ï¿½ï¿½ï¿½uï¿½{46ï¿½FzCï¿½ï¿½ï¿½ï¿½Zï¿½Ò¥ï¿½ï¿½ ï¿½ï¿½.ï¿½^Mï¿½ï¿½S iï¿½ï¿½g3/4Pï¿½ï¿½ï¿½ F`1/2eï¿½snï¿½6ï¿½ï¿½[;CILÉï¿½ 1/21ï¿½`ï¿½ï¿½yï¿½Rï¿½Vcï¿½4ï¿½Nï¿½ ï¿½Hlï¿½ï¿½Yï¿½ï¿½3v ï¿½ï¿½W.ï¿½yï¿½ï¿½Ç£YrI*IbEï¿½ï¿½%U<ï¿½<ï¿½ï¿½ï¿½ ï¿½ 'Gï¿½ï¿½9'9¡_1ï¿½...ï¿½.-iï¿½ï¿½J\P)Lï¿½ï¿½2ï¿½ï¿½[email protected]ï¿½ï¿½ï¿½ï¿½2Wï¿½,>ï¿½'{L"ï¿½nï¿½Iï¿½ï¿½Í[email protected]"y{ï¿½k{ ï¿½!gï¿½ï¿½kxï¿½CÆkCï¿½ï¿½Qcï¿½ëµï¿½ jï¿½Rï¿½ï¿½tï¿½ï¿½Gï¿½-(r)ï¿½'+ ?-|#p(r)qï¿½(ï¿½ï¿½>>ï¿½ï¿½ ...Kï¿½ï¿½ï¿½ï¿½ï¿½*"ï¿½"×¨Y-(tm)W)sï¿½ï¿½ Ìº1/4ï¿½ï¿½G)h8ï¿½ï¿½ï¿½Qï¿½Vï¿½R(tm)ï¿½ï¿½8-EÑ­b3/4h2ï¿½ï¿½ï¿½UÐ!'ï¿½ï¿½mï¿½rï¿½ :ï¿½e×KQuï¿½ï¿½ï¿½ï¿½]ï¿½1ï¿½n|HXï¿½ï¿½E.ï¿½1...--"cï¿½ï¿½`)ï¿½ï¿½ï¿½~ï¿½ï¿½uï¿½ï¿½k\$`)8',EV7ï¿½Lï¿½bï¿½σï¿½ oï¿½ï¿½!ï¿½`) )ï¿½dï¿½"Wï¿½Rï¿½ï¿½ -'6,e~ï¿½I.ï¿½Tï¿½,R-9ï¿½ï¿½l%ï¿½ËÆï¿½ ï¿½ï¿½Sï¿½Zz " U-1/4aï¿½;w tï¿½[email protected]'ï¿½p dï¿½Zï¿½e,Òï¿½ï¿½Gï¿½ï¿½Pï¿½ V ï¿½>9zTï¿½ï¿½ï¿½ï¿½ï¿½*ï¿½2ï¿½iï¿½ï¿½ï¿½ï¿½Sï¿½ï¿½ï¿½ï¿½6ï¿½ ï¿½ Gï¿½[;ï¿½bï¿½ï¿½ï¿½Opï¿½ï¿½4>ï¿½ï¿½De (tm)ï¿½ï¿½bï¿½i'yï¿½Ü§ï¿½ï¿½'8Bsï¿½! .Dï¿½R,/dï¿½eï¿½g ï¿½ bï¿½< ï¿½+ï¿½ sï¿½r}ï¿½? ï¿½ï¿½hï¿½"}ï¿½|ï¿½<lEï¿½b ï¿½ï¿½ï¿½0ï¿½[Cï¿½ï¿½ ï¿½+0ï¿½ï¿½ï¿½%{Èï¿½ ï¿½f^gï¿½ï¿½MMï¿½Kï¿½'ï¿½ï¿½ ï¿½3fBï¿½ï¿½ï¿½\+'>5ï¿½ï¿½ï¿½ï¿½ï¿½lx93ï¿½dï¿½<ï¿½ï¿½Yï¿½ï¿½ï¿½v{"8ï¿½Åï¿½rkï¿½V=ï¿½ï¿½ï¿½k`"ï¿½ï¿½ï¿½A'ï¿½ï¿½ï¿½'1/2ï¿½?Uf=ï¿½ï¿½ï¿½)lG...ï¿½ï¿½-("ï¿½1/2ï¿½l1¶uï¿½ ï¿½ï¿½ï¿½ï¿½Ñ­"vï¿½ ï¿½{&ï¿½qï¿½~ï¿½1/2ï¿½1/4ï¿½l4lï¿½> ï¿½Z"sï¿½ï¿½Zï¿½ï¿½qï¿½Zï¿½xru%ioU29/'bï¿½ ï¿½ï¿½ëª¡ï¿½ï¿½ï¿½ï¿½:ï¿½ï¿½"aï¿½m_Lj<ï¿½ï¿½ ï¿½wï¿½Ó1/2ï¿½ï¿½ï¿½ï¿½ Fl ï¿½'\ï¿½[email protected]ï¿½ï¿½ï¿½"0^kï¿½(r)ï¿½Eï¿½ï¿½ï¿½M-Vï¿½Rï¿½ï¿½ï¿½ï¿½ï¿½b'Å1ï¿½ï¿½ Ñ£ï¿½&v'uGz`ï¿½ï¿½{b

1. ## Maths Internal Assessment -triangular and stellar numbers

The 'R' value is the accuracy of the plotted data when compared to the polynomial trend-line. This value state 1 which means that it is 100% accuracy which supports the equation by stating that it is 100% accurate. The graphs below display the other values of 'p' to test the validity of this equation.

2. ## Math IB SL BMI Portfolio

Looking at this graph, one can come to the conclusion that it will take more than one mathematical function to graph the entirety of the data. If one were to relate the concept of human growth with the measurable value of BMI, then there is a problem in assuming the

1. ## Stellar numbers

As with the 6-vertices there are two layers, the pentagon then the extensions of the pentagon. Hence, The "1" is removed at the start in order to maintain consistency, the similar constructions warrant this action. Due to similar constructed nature, it shall be also be multiplied by 2.

2. ## Stellar Numbers. After establishing the general formula for the triangular numbers, stellar (star) shapes ...

+ 11 Vn = an2 + bn + c Vn = 6n2 + bn + 1 V1 = (5)(1)2 + b(1) + 1 1 = 5 + b + 1 b = - 5 ? Sn = 5n2 - 5n + 1 Vn = 5n2 - 5n + 1 V3 = 5(3)2 - 5(3)

1. ## Stellar Numbers Investigation Portfolio.

�2] x [2 x 10 + (n - 2) 10] S2 = 1 + [(2-1) �2] x [20 + (2 - 2) 10] S2 = 1 + [1 �2] x  S2 = 1 +  S2 = 11 Using the general statement it is possible to calculate that S2 of the 5- Stellar star has 11 dots in it.

2. ## Stellar Numbers Portfolio. The simplest example of these is square numbers, but over the ...

I decided to try for 5-stellar numbers, that the formula would be 5n2-5n+1. After plugging in numbers to this formula until up to S8 and seeing that all of them worked, the validity of this formula had been tested and proven. • Over 160,000 pieces
of student written work
• Annotated by
experienced teachers
• Ideas and feedback to 