This is an investigation about stellar numbers, it involves geometric shapes which form special number patterns. The simplest of these is that of the square numbers (1, 4, 9, 16, 25 etc…) The diagram below shows the stellar triangular numbers until the 6th triangle.

The next three numbers after T5 would be: 21, 28, and 36.
A general statement for nth triangular numbers in terms of n is:

The 6-stellar star, where there are 6 vertices, has its first four shapes shown below:

The number of dots until stage S6: 1, 13, 37, 73, 121, 181
Number of dots at stage 7: 253
Expression for number of dots at stage 7:
Since the general trend is adding the next multiple of 12 (12, 24, 36, 48 etc…) for each of the stars, so for S2 it would be 1+12=13, and for S3 it would be 13+24=37

General statement for 6-stellar star number at stage Sn in terms of n:

For P=9:

Since S1 must equal 1 then we can prove this formula by showing that:

So the first six terms are: 1, 19, 55, 109, 181, 271
Therefore the equation for the 9-Stellar star at

For P=5:

Since S1 must equal 1 then we can prove this formula by showing that:

So the first six terms are: 1, 11, 31, 61, 101, 151
So the expression for 5-Stellar at

General Statement for P-Stellar numbers at stage Sn in terms of P and = For P-Stellar number equals 10:

For P-Stellar number equals 20:

The General Statement works for all number fro 1 to positive infinity. The equation was arrived at since the sum of arithmetic series can be found using , since the difference is always 2P then we can replace 2P with d, and since u1 is always equal to 1, we can replace it with 1 every time. The at the end of the equation serves the purpose of making the difference between the numbers in the series constant. This form of the equation will allow for only one variable to change, which will be . One of the things the student realized while solving this...

...STELLARNUMBERS
In order to develop this mathematics SL portfolio, I will require the use of windows paint 2010 and the graphic calculator fx-9860G SD emulator, meaning that I will use screenshots from this software with the intention of demonstrating my work and process of stellarnumbers sequences.
Triangular numbers are those which follow a triangular pattern, these numbers can be represented in a...

...understanding. Based on geometry alone, many special patterns evolve, such as the square numbers, triangular numbers, and much more. The StellarNumbers are mostly used in astronomy and astrology. StellarNumbers are figurate numbers based on the number of dots that can fit into a midpoint to form a star shape. The points of the star determine the number of points...

...this following assignment, I will be considering geometric shapes that lead to special numbers. The simplest examples of these are square numbers (1, 4, 9, 16, etc), which are derived from squaring 1, 2, 3, and 4. From this I got the equation y= x2. This equation is illustrated in the table below.
y=x2
|x |y |
|1 |1 |
|2 |4...

...
StellarNumbers
Results
1. Triangular Numbers
Observation of the number pattern of polynomial type or different pattern needed.
Identifying the order of the general term by using the difference between the succeeding numbers.
Students are expected to use mathematical way of deriving the general term for the sequence.
Students are expected use technology GDC to generate the 7th and 8th terms...

...to special numbers. The simplest example of these are square numbers, such as 1, 4, 9, 16, which can be represented by squares of side 1, 2, 3, and 4.
Triangular numbers are defined as “the number of dots in an equilateral triangle uniformly filled with dots”. The sequence of triangular numbers are derived from all natural numbers and zero, if the following number is always added...

...Student ID: 22087885
Exam: 986093RR - Business Math, Part 2
1. Ann works 51/2 hours, Mary works 61/3 hours, and John works 41/4 hours. How many combined hours
have they worked?
A. 165/12
*B. 161/12
C. 151/12
D. 155/12
2. You pay the following for supplies: $19.36 for pens; $21.75 for notepads; and $32.26 for computer
paper. What is your total?
A. $73.73
B. $77.37
C. $77.73
*D. $73.37
3. How many liters will a U.S. 6-quart container...

...MathIAMath Internal Assessment
EF International Academy NY Student Name: Joo Hwan Kim Teacher: Ms. Gueye Date: March 16th 2012
Contents
Introduction Part A Part B Conclusion
Introduction
The aim of this IA is to find out the pattern of the equations with complex numbers by using our knowledge. I used de Moivre’s theorem and binomial expansion, to find out the specific pattern and make conjecture about it. I...

...IA Task I
Introduction and purpose of task: The purpose of this task is to investigate the positions of points in intersecting circles and to discover the various relationships between said circles. Circle C1 has center O and radius r. Circle C2 has center P and radius OP. Let A be one of the points of intersection of C1 and C2. Circle C3 has center A and radius r (therefore circles C1 and C3 are the same size). The point P’ (written P prime) is the intersection of C3 with...

507 Words |
2 Pages

Share this Document

{"hostname":"studymode.com","essaysImgCdnUrl":"\/\/images-study.netdna-ssl.com\/pi\/","useDefaultThumbs":true,"defaultThumbImgs":["\/\/stm-study.netdna-ssl.com\/stm\/images\/placeholders\/default_paper_1.png","\/\/stm-study.netdna-ssl.com\/stm\/images\/placeholders\/default_paper_2.png","\/\/stm-study.netdna-ssl.com\/stm\/images\/placeholders\/default_paper_3.png","\/\/stm-study.netdna-ssl.com\/stm\/images\/placeholders\/default_paper_4.png","\/\/stm-study.netdna-ssl.com\/stm\/images\/placeholders\/default_paper_5.png"],"thumb_default_size":"160x220","thumb_ac_size":"80x110","isPayOrJoin":false,"essayUpload":false,"site_id":1,"autoComplete":false,"isPremiumCountry":false,"userCountryCode":"US","logPixelPath":"\/\/www.smhpix.com\/pixel.gif","tracking_url":"\/\/www.smhpix.com\/pixel.gif","cookies":{"unlimitedBanner":"off"},"essay":{"essayId":36281254,"categoryName":"Periodicals","categoryParentId":"17","currentPage":1,"format":"text","pageMeta":{"text":{"startPage":1,"endPage":2,"pageRange":"1-2","totalPages":2}},"access":"premium","title":"Math Ia Type 2 Stellar Numbers.","additionalIds":[13,157,19,2],"additional":["Health \u0026 Medicine","Health \u0026 Medicine\/Pharmaceuticals","Natural Sciences","Awards \u0026 Events"],"loadedPages":{"html":[],"text":[1,2]}},"user":null,"canonicalUrl":"http:\/\/www.studymode.com\/essays\/Math-Ia-Type-2-Stellar-Numbers-1169135.html","pagesPerLoad":50,"userType":"member_guest","ct":10,"ndocs":"1,500,000","pdocs":"6,000","cc":"10_PERCENT_1MO_AND_6MO","signUpUrl":"https:\/\/www.studymode.com\/signup\/","joinUrl":"https:\/\/www.studymode.com\/join","payPlanUrl":"\/checkout\/pay","upgradeUrl":"\/checkout\/upgrade","freeTrialUrl":"https:\/\/www.studymode.com\/signup\/?redirectUrl=https%3A%2F%2Fwww.studymode.com%2Fcheckout%2Fpay%2Ffree-trial\u0026bypassPaymentPage=1","showModal":"get-access","showModalUrl":"https:\/\/www.studymode.com\/signup\/?redirectUrl=https%3A%2F%2Fwww.studymode.com%2Fjoin","joinFreeUrl":"\/essays\/?newuser=1","siteId":1,"facebook":{"clientId":"306058689489023","version":"v2.8","language":"en_US"},"analytics":{"googleId":"UA-32718321-1"}}