Pascal 's Triangle : Special Mathematical Properties

Blaise Pascal was a brilliant mathematician and experimenter, and he was the voice that still protested against the new science and the materialism of Descartes. His investigations of probability in games of chance produce his very own theorem, and his research in conic sections helped lay the foundations for integral calculus.

“Home” is something that people desire to have; one often looks to other people and places in an attempt to fulfill this desire. Most people characterize themselves based upon their home and therefore transform their identity, whether it be because they are trying to conceal their home or trying to flaunt it. In both The Glass Castle, by Julia Walls, and The Absolutely True Diary of a Part Time Indian, by Sherman Alexie, the protagonists’ identities are affected by their own perception of home. Through these two novels, the authors emphasize the importance of a stable home, as well as the internal struggle of following your desires to shape your identity.

And to offset his good looks, the H-G men required that he wear at all times

Understanding place value is integral to mathematics, and is especially for addition and subtraction. Being able to easily rearrange numbers between place values is required for most addition and subtraction problems. Part of grasping place value is being able to unitize. Fosnot and Dolk explain unitizing to be “a child’s construction of the logic to think of 10 flexibly as ten 1’s or as one unit of 10” (Taylor, Breck, & Aljets, 2004, p. 140). Unitizing is what makes “borrowing” in subtraction possible. If a problem is 32 – 16, one of the three tens must be broken up into units in order to subtract; being able to see 32 as 3 tens and 2 ones and as 2 tens and 12 ones is what makes the problem possible. Place value and unitizing have much to do with a comprehension of base ten, but they are not exclusive to base ten. For example, one could apply the idea of place value and unitizing to base five. The number 18510 would be written as 12205. The place values would then be 125, 25, 5, and 1 (instead of 1000, 100, 10, and 1), and 12205 would be understood as one 125, two 25s, and two 5s. Unitizing would allow for someone to

For over ten years or more, I have known Ms. Delois Bynum as a person full of wisdom with inspiring words. She’s cheerful, graceful and amusing and I am delightful that over the years her demeanor hasn’t changed. When someone is in need she doesn’t fall short in helping him or her. Moreover, she’s full of energy because Ms. Bynum gets daily exercise by walking and greeting her neighbors.

“I counted everything. I counted the steps to the road, the steps up to church, the number of dishes and silverware I washed … anything that could be counted, I did,” (Nasa.gov). These words, spoken by Katherine Johnson, reveal her love for math as a child that would continue through her adult life. Born in 1918 in White Sulfur Springs, West Virginia, Katherine loved anything to do with math for as long as she could remember. She was eager to go to school and start learning, and she ended up advancing straight into second grade. In addition to this amazing feat, she started high school at age 10 and college at age 15. This in itself is an incredible accomplishment considering her age, but it’s even more incredible when taken into account that most black children at the time didn't go beyond 8th grade. She studied at West Virginia State College to become a mathematician and graduated when she was 18, an age

The article, “Punch Up Algebra with POWs,” by Mark Pinkerton and Kathryn Shafer begins by stressing the importance of problem solving abilities since it leads to understanding mathematical concepts. The authors stress that students need to be given the opportunity to “reason and make sense of mathematics.” The article examines co-author, Mark Pinkerton’s, yearlong experience that was designed to provide constant problem solving opportunities for his students. (Pinkerton & Shafer, 2013).

The basic elements of Heclo’s issue networks idea is power and control. The difference between issue networks and iron triangle. Issue networks operate at many levels, from vocal minority who turn up at local planning commission hearings to the well-known professor who is invited to read at the White House. Issue networks are more public and focus more on national policy such as income redistribution abortions, drug legislation, gun control, and world hunger. Iron triangles and sub governments assumes small circles of participants who have succeeded in becoming largely self-sufficient. Iron triangles and sub governments suggests a stable set of participants united to control narrow programs which are in the direct economic interest of

Homicide, mental breakdowns, and inequalities all occurred in an abandoned home, the short story Trifles by Susan Glaspell is a dark tale about a wife and her suspected killing. A sheriff, county attorney, and two old friends all investigate Mr. and Mrs. Wright's home to find clues about the murder. More was found about MRs. Wright and her motives behind her assumed killing.

People say that love is something extremely powerful and miraculous; it is a language that the blind can see and the deaf can hear. Director Marcel Carné attempted to show that love has the ability to change a person in many different ways in his movie Le quai des brumes (Marcel Carné , 1938). This attempt is most evidently presented in the sequence of Jean meets the ship doctor, who invites him to sail to Venezuela with him on the port; and the sequence following, in which Jean goes to the carnival with his lover, Nelly.

She published philosophical works clarifying facts and generalizing the into laws to form a system of sociology and psychology. Years later, Germain was the first person to provide proof of Fermat’s Last Theorem, that has been a struggle for mathematicians for the past 200 years. “That if xn + yn = zn, then neither x, y, nor z can be a natural number if n is greater than 2, stated from Fermat's Last Theorem" (Barrow-Green). Germain used her proficiency on prime numbers to help to prove this theorem. Successful from her work, she published her deeds in a supplement to her acquaintance Adrien-Marie Legendre's work Théorie des nombres.” (The Remarkable Life of Sophie Germain)

Communication In her search for a solid identity, Charlotta has to find features that would characterize her as her own distinct individual person. That is why she always acts with an extreme temperament (the volatility and unpredictability which are Dionysian and Folly qualities). Sometimes she appears to be a narcissistic and tyrannical character, criticizing everyone around her (e.g. what she says about singing refugees: “These people, they sound like hyenas.”). At other times she is a very sensitive individual exposing her most intimate thoughts (e.g. “I long to have someone to talk to but there isn’t anybody.”)

I firmly believe that the theory concerning the magical properties of the number seven invented by the 'Mother of Magical Arithmancy' Bridget Wenlock to be the most important discovery to occur in the field of Arithmancy. 'The Theory of the Number Seven' is basically instances in which the magic that surrounds the number becomes clear. For example, the age at which a witch or wizard generally shows their first signs of magic, the number of obstacles put in place to protect the Philosopher's Stone, and the number of years of schooling availlable here at Hogwarts, are all occasions where the number seven is present.

Multiplication by ten gives students opportunity to explore larger numbers, and can also be extended on(Reys et al. ch. 11.4). In addition, multiples of 10 give students the knowledge that all digits move left one place and an additional place hundreths. This concept can be used to introduce the decimal place which is also moving place each time something is multiplied by tens. Exposing students to a range of examples which displays patterns that occur when multiplying by tens and hundreths will generate meaning of digits moving place (Reys et al., ch. 11.4).

     Another example happened during one of my Calculus classes that I believe to be the most abstract and creative of the maths. A fellow student and me figured out pie. We figured out that the integral from 0 to1 of the square root of x minus 1 is equal to half of pie. We had huge problems figuring out this