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EMM111 Maths And Numeracy Assignment 2: Investigation Seminars.

What Are Happy Numbers?. A happy number is when you think of any number.Square each of the numbers digits and add the squares to get a second number.Repeat process number two on the second number, and add the squares to get a third number.Continue this process until a sequence is formed.For exam

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EMM111 Maths And Numeracy Assignment 2: Investigation Seminars.

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    1. EMM111 Maths And Numeracy Assignment 2: Investigation Seminars.

    2. What Are Happy Numbers? A happy number is when you think of any number. Square each of the numbers digits and add the squares to get a second number. Repeat process number two on the second number, and add the squares to get a third number. Continue this process until a sequence is formed. For example: 7’s sequence is: 7,49,97,130,10,1 If a sequence reaches 1, then the number is HAPPY, if it doesn’t the number is SAD.

    3. How to Calculate Happy and Sad Numbers. (A Practical Example) Eg/ 7= 7*7 = 49 49=4*4 + 9*9 =97 97= 9*9 + 7*7 = 130 130= 1*1 + 3*3 + 0*0 = 10 10= 1*1 + 0*0 = 1 1= HAPPY NUMBER.

    4. Processes of Investigating Happy Numbers. The first weeks two weeks involved problem solving with a partner. During the two weeks all that are achieved was knowing what numbers are happy from one to thirty. I then consulted with Craig to see if a formula could be created to find Happy Numbers but after hours of trying a formula could not be reached. After this consultation it became clear that other alternatives would need to be used to find out what numbers are happy and sad. I began calculating the answers manually using a calculator but after two hours and twenty numbers later I decided that there would need to be a better alternative. I began researching on the internet and found the website : www.wschnei.de/digit-related-numbers/ happy-numbers-list.html This site was my life saver as it gave me all the happy numbers to one thousand. This allowed me to focus on how Happy Numbers occur rather then what are the happy numbers.

    5. The Results.

    6. Happy Numbers Continued.

    7. What Does This Tell Us: What Proportion of numbers are happy: 1-20 = 11 happy numbers = 55% 1-100= 20 happy numbers = 20% 1-1000= 142 happy numbers = 14.2%

    8. Predicting Numbers. Can you predict if any numbers will be happy or sad? Yes and NO Rules Associated with Calculating Happy Numbers: Numbers with the same digits will provide the same results eg/ 319 & 931 are both happy numbers. The 0 digit has no impact or implication on the result. When calculating happy numbers all the numbers in the sequence leading up to one are happy numbers eg/ 7,49,130,10 & 1 are all happy numbers. For every happy number when you add a 0 the number also becomes happy eg/ 13 and 130 are both happy numbers. Myths about calculating happy numbers; - All Happy Numbers are divisible by 7 - Digits add up to 10

    9. Is There a Cycle (how do I know when to stop) During manual calculations I noticed a cycle developing that showed when a number was sad. There was a 8 number cycle that continually rotates and a number can’t escape. The cycle is:

    10. Investigation Summary. The Processes that I undertook to complete the Investigation & the questions that I tried to answer were: What is a Happy & Sad Number? How do I calculate the numbers? What are the Happy Numbers? Does the Percentage of Happy numbers increase or decrease as we investigate more numbers? Are there any rules that help us calculate Happy numbers? Can we Predict Happy Numbers? How do we know when a number has no chance of becoming Happy? What is this cycle? Provide a table of Happy Numbers to see if any one else can see a pattern.

    11. Conclusions. The majority of numbers are sad. I couldn’t find a formula to solve the investigation or tell us what numbers are happy or sad. You can predict happy numbers by knowing the results certain digits grouped together produce. Sad numbers produce a 8 number cycle so when you reach a number twice you know it is sad. Numbers with the same digits produce the same results. Giving a class full of students this investigation could keep them intrigued and mentally busy for hours.

    12. Evidence of E-Portfolio Inclusion To see this PowerPoint presentation on my E-Portfolio it can be seen on the website : http://athene.riv.csu.edu.au/~btoole02/

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