# Happy Numbers Essay

911 words - 4 pages

I chose this topic because it sounded like an interesting topic and it was a part of math I didn’t know about. Happy numbers are a part of recreational maths.
In this report I will be talking about happy numbers, these are numbers that when you square the digits of the number and add the squares together repeatedly, in the end you will end up with one. I will also talk about happy cube numbers, they are the same as happy numbers, but instead of squaring the digits of the original number, the digits are cubed. Furthermore, I will also explore happy prime numbers, these are prime numbers which are also happy. Additionally, I will mention unhappy numbers, these are numbers that do not end in ...view middle of the document...

1 is a special number because once it reach 1 it will remain there, because 1²=1, so it will always remain the same.`
Happy numbers are part of a set of numbers. If the number is seen as N and the digits M , then M²=N₁, M₁²=N₂…….until …..Mx²= 1. N≠0.
If a number is a happy all numbers in the sequence are also happy. So since 19 is happy 82, 68, 100 and 1 are also happy numbers.
Any permutation of the digits of a happy number also leads to a happy number. An example is 13 is a happy number ¹P₁=1, ³P₃=6. 1+6=7, 7 is a happy number.
All numbers that are 10ˣ are also happy numbers, this is because their digits will always be one 1 and one or more 0’s. an example would be 10²=100 and 100 is a happy number.
Furthermore if a happy number N has one more zero added to the end of it, it will still be a happy number this is because zero does not affect the sum of the squares. An example is 13 is a happy number and so is 130.
The first few happy numbers are 1, 7, 10, 13, 19, 23, 28, 31, 32, 44, 49, 68, 70, 79, 82, 86, 91, 94, 97, 100…..

Unhappy numbers
Unhappy numbers are numbers that after having their digits squared and added together repeatedly the number always leads to 4. This is how you find out if a number is unhappy:
16:
1²+6²= 1+36= 37
3²+7²= 9+49= 58
5²+8²= 25+64= 89
8²+9²= 64+81= 145...

## Find Another Essay On Happy Numbers

### Betting the Lottery Essay

3892 words - 16 pages The best way to bet the lottery is by not too.If you do, and if you keep track, you will eventually become convinced that you shouldn't bet the lottery for real at all.Why? Because you simply cannot guess the winning numbers often enough.Sound familiar?* "If I do win, the payoff will be a lot more than what I've spent."* "Someone has to win."If you use these rationales or any others to explain to yourself why you spend time and money buying

### Organizational Financial Analysis Examine programs that provide solutions to today’s health care problems Evaluate the impact of the choice on global health care options and the impact of fraud on the...

2419 words - 10 pages . Although Happy Hospital did not have any debt coming into the year 2008, they did begin to take on some as the year progressed. The solvency and profitability numbers reflect two years of difficult income. The negative interest and debt service ratios indicate that the hospital did lose money. In addition, operating and total losses have created a negative profitability ratio. These are all indicators that Happy Hospital will have to work hard in

### The atchison corporation A, B, C

855 words - 3 pages much different and it's very confrontational. In most change situation this approach is not effective and cause lots of cultural crisis as we see in the case. But with a new format and a smooth pace it could happen in a better way, because the organization culture shaped during the years and it can't be changed in a night and instead of long term profitability he must be kept in mind to keep current employees happy and positive.The first thing I

### Was the nazi regeme beneficial to German women?

945 words - 4 pages the home. These groups were not compulsory either and the rapid growth in numbers (12 million by 1939) showed the women were happy and willing to go to these groups. These groups also offered the opportunity of being a group leader, giving women a lot of pride. The Nazis Also introduced the Honour Cross Of German Motherhood for mothers who had had more than 4 children encouraging German birth but also giving women something to aim for. This was

### wewew

515 words - 2 pages Names: Rui Zhi ZhaoStudent Numbers: 055-051-130Date: Nov 5, 2014Course: IPS355Section: BBProfessor: William WeissglasRe: Journal #4 - Active Constructive Responding & ListeningOTHERS EVENT #1My co-worker shares an event---"I went back to China last month."My response---"Really!,that is awesome.I am so happy that you can go back to China.How was it ? Where did you go??"My co-worker response---"It was really amazing! I went back my hometown

### CPI: Fluctuation of Price of Goods and Services in a Country

1406 words - 6 pages getting the numbers of change in price of the fixed price of goods. Once that is done the numbers are then averaged which then leads to weighing them based on how important the good is. The changes that do occur in these numbers are then related to the changes that occur in cost of living. Such as if the prices of oil goes up it will be reflected in these numbers as fuel is a very important aspect of living cost whether it means for your car or

### title

1009 words - 5 pages the game in September of 2005. UC DAVIS AND ME. I personally would be happy to go to UC Davis, if I lived in the area. But at the moment, I don’t live in California and don’t find the school to be worth the effort of gaining residency. The University boasts good numbers in academics, athletics, and student satisfaction with the school, but once again it just isn’t worth the cost. If I were able to attend the school without the concern of gaining

1287 words - 5 pages , “the absurd variety of his fans is, as ever, unmatched in sports” (19). Rushin’s statement explains the variety of fans that Jordan has collected throughout his career as a basketball player and how these fan numbers tower over any other sport. It is predictable that the fans will want to see Jordan play again and Roscoe Nance, from USA Today, proves this by mentioning the boom in ticket sales after his return. Nance reports, “Ticket sales say

1337 words - 5 pages the queen for punishment because of his sexual scandals in France. It is easy to enjoy the film without placing much thought into the purpose of the musical numbers that are so carefully positioned within the film, or into the duality of the main characters who are so carefully stacked beside one another and are balanced throughout the film. However, to those who are knowledgeable of the way musicals are constructed, the first song, sang by Count

### The Value of Humanity

1777 words - 7 pages therefore morale. With every negative experience, especially on a grand scale, such as atrocities like crimes against humanity, the numbers go down and decrease hope. It is quite simple, in fact. In order to have a happy world, these numbers should stay positive. This relates to a quote on page 168 of First They Killed My Father. Loung Ung says,“I need the new memories that make me angry to replace the old ones that make me sad. My rage makes me

### Stumbling on Happiness by Daniel Gilbert - Book Report

1209 words - 5 pages the world with a desire for control. Imaginging the future allows us to control or change what is about to happen to us.Gilbert makes the case that happiness is a subjective feeling and it is therefore not possible to define or compare the levels of happiness between two people. To an outsider, Lori and Reba, the conjoined twins, may look sad and unhappy, but they are in fact happy in their situation. But surely, we can compare our own levels of

## Similar Essays

### You Are Not A Number Essay

1185 words - 5 pages to be happy. Moreover, a name, which is a word, has one or more meanings while numbers do not have any meaning at all.One fundamental question to ask when disproving the statement is ?Can feelings and emotions be calculated?? A person may say ?On a scale from 1-100, my love for you is 99.99.? to express his/her love in a striking way. But such a statement is not understood literally. It is a figure of speech used to represent how great one?s love

### Money And Power Don't Bring Happiness

4246 words - 17 pages people who find family rather important are most likely to be quite happy, and people who find family not very important are most like to be quite or not very happy. Strangely enough though, there is a higher percentage of people who are very happy who say they don’t value family at all when compared with the other two categories. We find that the exact same is true for the importance of friends. While the numbers are not exact, they are

### Georg Cantor Essay

2044 words - 8 pages I. Georg CantorGeorg Cantor founded set theory and introduced the concept of infinite numbers with his discovery of cardinal numbers. He also advanced the study of trigonometric series and was the first to prove the nondenumerability of the real numbers.Georg Ferdinand Ludwig Philipp Cantor was born in St. Petersburg, Russia, on March 3, 1845. His family stayed in Russia for eleven years until the father's sickly health forced them to move to

### Georg Cantor Essay

2044 words - 8 pages I. Georg CantorGeorg Cantor founded set theory and introduced the concept of infinite numbers with his discovery of cardinal numbers. He also advanced the study of trigonometric series and was the first to prove the nondenumerability of the real numbers.Georg Ferdinand Ludwig Philipp Cantor was born in St. Petersburg, Russia, on March 3, 1845. His family stayed in Russia for eleven years until the father's sickly health forced them to move to