Fraction Differences
First Sequence
To begin with I looked at the first sequence of fractions to discover
the formula that explained it. As all the numerators were 1 I looked
at the denominators. As these all increased by 1 every time, I
figured that the formula was simply [IMAGE] as the denominators
corresponded to the implied first line as shown in this table below:
nth number
1
2
3
4
5
6
7
8
Denominators
1
2
3
4
5
6
7
8
I shall call this Formula 1 (F1) for easy reference.
Second Sequence
[IMAGE] [IMAGE] [IMAGE] [IMAGE] [IMAGE]
Again I decided to discount the numerator as it was 1, and I decided
to concentrate on the differences between the denominators rather than
the ‘fractions’. So I am looking for a formula that will explain the
sequence: 2, 6, 12, 20, 30.
First of all though I decided to extend the sequence in order to have
a broader range to work with. I used a calculator to work out the
following denominators finding the difference between [IMAGE] and
[IMAGE], [IMAGE] and [IMAGE] all the way up to [IMAGE]
I set the differences out in a table to try to find the pattern:
nth number
1
2
3
4
5
6
7
8
9
Sequence
2
6
12
20
30
42
56
72
90
First Difference
4
6
8
10
12
14
16
18
Second Difference
2
2
2
2
2
2
2
2
retrieved from 6 and 6 when the number is 12, in whole numbers. I will
Have you ever read a book to prepare for the movie coming out, but when you watch the movie all you can do is compare the two. It’s the utmost distressing part because you expected the book, but you gain a new version of it and sometimes it’s not as exceptional. Sometimes they leave out important characters, or they leave out cool events, or sometimes the message isn’t the same. This will be comparing Devil’s Arithmetic.
It is possible to use the recursive pattern and equation an= 2an-1+1 to find the answer but in order to do this, one needs to know what “a” is. This reveals a weakness in recursive patterns because in order to know what “a” is for 64 discs, one must know “a” for 63 discs, “a” for 62 discs, and so on. This process would be very time consuming and therefore not an efficient way of solving the problem. Graphing the data to compare the # of discs with the Total Moves would also be impossible. This is because “a” is unknown unless the previous terms are known. Therefore it would be impossible to graph a recursive equation simply because their
The Golden Proportion is defined geometrically as the ratios, where the ratio of the whole segment to the longer segment is equal to the ratio of the longer segment to the shorter segment. Mathematically, the precise value of this Ratio is expressed as 1.6180339887...,a never-ending number which goes to infinity. Thus this ratio cannot be expressed as a whole number or as a fraction and is considered an irrational number. If drawing algebraically, the point C divides the line AB in a certain way that the ratio of AC to CB is equal to the ratio of AB to AC. The algebraic calculation shows that the ratio of AC to CB and AB to AC equals 1.618… whilst the ratio of CB to AC is equal to
It is mentioned in the Qur’an that “those who believe (in the Qur’an), and those who follow the Jewish (scriptures), and the Christians and the Sabians… Shall have their reward with their Lord” (2:62) which implies that all who believes in the Abrahamic religion, follow the holy books, and believe in Allah shall be rewarded, for all the Abrahamic religion is derived from the same source; Abraham and believes in the same God. Through the eyes of a Muslim, there are core fundamentals that define whether a person is favorable as one of the “People of the Book.” Although Augustine presents many similar view of religion as Islam, Mohammed will not be that favorable in considering Augustine as one of the “people of the book” simply because the basic fundamentals of Augustine’s beliefs do not coincide with Islam. The deification of Jesus, for example, is a strikingly contrasted view compared to what the Qur’an states. Another example would be his decision to abandon his professorship in rhetoric and instead just serve god. Lastly, he also presents a view that it is more favorable for a man of a higher stature to convert than a normal person, which is clearly not the case with Islam.
Short stories are a form of literature works that authors use to communicate various themes and issues to the reader. As such, it is common for different short stories authored by different people to have a central meaning or theme that differs from each other. In addition, the way the author portrays his/her central theme or meaning would differ from the way other authors would craft their short stories to best portray their central meaning. While some would use characterization as a means of portraying the theme of their story, other authors employ the use of symbols to better communicate their theme. However, some slight similarities can always be drawn between short stories. ‘Hills like White
The stories Remembering My Childhood on the Continent of Africa and Self-Discovery and the Danish Way of Life are easily comparable. The narrators of both stories write about a time in which they are experiencing a different culture. They also write about their yearnings for self-discovery through exotic experiences. The viewpoints, however, of each writer are at opposite ends of the spectrum. In Self-Discovery and the Danish Way of Life, the narrator writes about his international experiences while studying abroad in Denmark. On the other hand, in Remembering My Childhood on the Continent of Africa, the narrator never actually visits Africa. Instead, he figuratively visits the continent through the experiences of another person. These stories may appear to be similar because of the comparable aspirations of the narrators. However, they are also different with respect the narrators’ unique viewpoints on life.
Some people think that if they could only change one aspect of their lives, it would be perfect. They do not realize that anything that is changed could come with unintended consequences. “The Monkey’s Paw” by W.W. Jacobs and “The Third Wish” by Joan Aiken both illustrate this theme. They demonstrate this by granting the main character three wishes, but with each wish that is granted, brings undesirable consequences. The main idea of this essay is to compare and contrast “The Monkey’s Paw” and “The Third Wish.” Although the “The Monkey’s Paw” and “The Third Wish” are both fantasies and have similar themes, they have different main characters, wishes, and resolutions.
The top 8 rows represent the group that ran with music the second time, and the bottom 8 are those who just ran two normal 40-yard dashes. The average speeds, in miles per hour, show how fast the runner was going during the entire 40 yard interval. The time change shows the difference in time elapsed between the two runs, and the rate change shows how much faster the runner ran the second time around.
It's helpful to know the difference between loving someone and "being in love," and it helps to do both in a relationship. People make a mistake in thinking of love as a steady, unchanging emotion. Being "in love" can transform into a deeper, constant desire to be together and share a life. But, as everyone knows, being "in love" doesn't always turn into a forever type of relationship. Passion over-rules compassion. The self is what matters the most.
Marriage is a word that instills a different meaning in every person that hears it. Some people think of the religious meaning, two people joined together in the eyes of God. Others don't involve a god into their union and see it as a union between two people. Occasionally people don't take marriage seriously and just consider it the next step after dating. Whatever the opinion, every person, whether married or single, has his or her own opinion of what a marriage is and what it entails. William Shakespeare, Judith Minty, and Linda Patsan all have their own ideas on marriage. In "Sonnet 116", "Conjoined", and "Marks," each express strong opinions on marriage. William Shakespeare's "Sonnet 116: Let Me Not to the Marriage of True Minds" states that true love is flawless and marriage that comes from that love is pure. Judith Minty's "Conjoined" maintains that marriage is unnatural and therefore restricts both person involved in it physically, spiritually, and emotionally. "Marks" by Linda Patsan supports that idea that marriage and motherhood are both hard work and deserve constant encouragement and appreciation instead of disapproval. The use of imagery, poetic devices, and diction depicts the authors' point in a powerful but still beautiful way.
Suksak, P. S. (2010, November 30). Catalan Numbers Presentation 2. Retrieved from Slide Share: http://www.slideshare.net/PaiSukanyaSuksak/catalan-number-presentation2
Usually in the game, only integers are used to make a result of 24. However, in some difficult 24 game questions, fraction calculation is required. For example: 2, 5, 5, 10 can be calculated as (5 − 2 ÷ 10) × 5 which is 24 over 5 multiplied by 5.
This is a trend table of industrial average financial ratio for the previous five years in comparison:
The golden ration can occur anywhere. The golden proportion is the ratio of the shorter length to the longer length which equals the ratio of the longer length to the sum of both lengths.