Math Mania

By: Nathan, Jacob, Nicole, George,

Amber, & Christina

Nathan Chess

Math Funnyz

SudokuNathan Chess

Music and Math

By: Nathan Chess

Ever wonder why some note combinations sound pleasing to our ears, while others make us cringe? To understand the answer to this question, you’ll first need to understand the wave patterns created by a musical instrument. When you pluck a string on a guitar, it vibrates back and forth. This causes mechanical energy to travel through the air, in waves. The number of times per second these waves hit our ear is called the ‘frequency’. This is measured in Hertz (abbreviated Hz). The more waves per second the higher the pitch. For instance, the A note below middle C is at 220 Hz. Middle C is at about 262 Hz.

Now, to understand why some note combinations sound better, let’s first look at the wave patterns of 2 notes that sound good together. Let’s use middle C and the G just above it as an example.

Now let’s look at two notes that sound terrible together, C and F#:

Do you notice the difference between these two? Why is the first ‘consonant’ and the second ‘dissonant’? Notice how in the first graphic there is a repeating pattern: every 3rd wave of the G matches up with every 2nd wave of the C (and in the second graphic how there is no pattern). This is the secret for creating pleasing sounding note combinations: Frequencies that match up at regular intervals

www.youtube.com/watch?v=JtSYIJb9Ukw

The Math Song

Nichole’s articleHelpful Study Tips

There are many ways to study for math and one of those ways

whether you no it or not is always right in front of you. Studying is as simple as taking your math book, sitting down and practicing

random problems from the math section you are working on. Math is not always the most fun thing to practice but with the help of

your friends from school it can be more fun then you think.When people don’t understand how to do math most of the time they are embarrassed to say that they don’t understand because they think people will make fun of them. If you are one of those

people then the first step is to admit that you have a problem and to get help. If you don’t want to say out loud that you don’t

understand wait until the teacher is through and approach her at her desk.

Another way to study for math is to take notes in class. Even if the teacher says you don’t have to take notes take them any way.

It makes it a lot easier to study and no what you are doing when you have the exact answers sitting in front of you. To find more

math tips Google them or go to various math sites.

There are 20 people on a bus heading for New York City, three of the people make stops along the way, five of them decide to go

straight through, and the rest of them decide to give up on the trip and just go home. How many people make it to New York, what group will make it there first and how many people go home?

8 people altogether will make it to New York City and The group of 5 make it there first. And then 12 people go home.

Nichole Secilia

Nicholes puzzle answer key

• Across Down

• 1. 55 1. 51

• 2. 90 2. 92• 3. 93 3. 91• 4. 72 4. 68• 5. 11 5.10• 6. 80 6. 82• 7. 40 7. 31• 9. 22 8. 74• 10. 51 9. 21• 11. 54 10. 42• 12. 12 11. 52• 13. 32 12. 14• 14. 103 13. 37• 15. 47 14. 44• 17. 64 15. 45• 18. 75 16. 23• 19. 63 17. 61• 20. 83 18. 73• 21. 57 19. 127• • • • • Nichole Secilia•

Nicholes Math cartoon

Careers using math

There are a lot of careers using math. In every job, you wave to use some type of math. Whether you are working at McDonalds or working

to rebuild a new skyscraper, you will use some type of math. Sometimes it is easy and sometimes it is very complicated. It is used to

determine the salary or to determine how big something is. One career that uses math a lot is drafting. In Drafting, you have to prepare drawings for many things. You design buildings and

structures. You also draw blueprints for companies. After the company gets a drawing request, then the drafting team starts working on it. It

could take hours, days, weeks, or months. Drafting & Design is a career field that uses a lot of math.

Another career that uses a lot of math is Culinary Arts. In culinary arts, you have to know the exact measurements for a recipe. If

you get a measurement wrong, then the recipe is wrong. You could mess it up by the slightest measurement error. Recipe measurements could be doubled or tripled also. You will have to adjust the recipe to

make the required servings. A big career that uses math is banking. You need to know how to do bank transfers. If the banker makes a mistake, then the account he/she is working on will be messed up. The amount in the account could be higher or lower than it really is. The banker needs to know

exactly what they are doing and how to do it right.

By George WhiteCareers using math

There are a lot of careers using math. In every job, you wave to use some type of math. Whether you are working at McDonalds or working to rebuild a new skyscraper, you will

use some type of math. Sometimes it is easy and sometimes it is very complicated. It is used to determine the salary or to determine how big something is. One career that uses math a lot is drafting. In Drafting, you have to prepare drawings for many things. You design buildings and structures. You also draw blueprints for companies. After the company gets a drawing request, then the drafting team starts working on it. It could take hours, days, weeks, or months. Drafting & Design is a career field

that uses a lot of math. Another career that uses a lot of math is Culinary Arts. In culinary arts, you have to know the exact measurements for a recipe. If you get a measurement wrong, then the

recipe is wrong. You could mess it up by the slightest measurement error. Recipe measurements could be doubled or tripled also. You will have to adjust the recipe to make the required servings.

A big career that uses math is banking. You need to know how to do bank transfers. If the banker makes a mistake, then the account he/she is working on will be messed up. The amount in the account could be higher or lower than it really is. The banker needs to know exactly what they are doing and how to do it right.

By George White

• Muhammad Al Khwarizmi. • His full name is Abū Abdallāh Muhammad ibn Mūsā al-

Khwārizmī. He was born around 780c. He died around 850c. He was around 70 years old when he finally

passed away. He is considered the father of algebra. Even though he was the father of algebra, there is not

much known about him.• They did discover a few things about him. A few things

they did find were about his family, his work, his life, and a few other details. He lived in Iraq, where at in Iraq

is unknown. He created math as we know it today so that is one important thing.

• He also published the first books of algebra. Al-Kitāb al-mukhtaṣar fī hīsāb al-ğabr wa’l-muqābala was his first book. It means The Compendious Book on Calculation by Completion and Balancing in his language. He also made other books. One more thing he did with his life

was revising Ptolemy version of geography. • Ptolemy wrote a book called Geography in the 2nd Century. It is a treatise on cartography and a compilation of what was known about the world's geography in the Roman Empire of the 2nd century. He also worked on

the Jewish calendar. The calendar describes the 19-year intercalation cycle, the rules for determining on what day of the week the first day of the month Tishrī shall

fall. • By George White

A confused bank teller transposed the dollars and cents when he cashed a check for Ms Smith, giving her dollars instead of cents and cents instead of dollars. After buying a newspaper for 50 cents, Ms Smith noticed that she had left exactly three times as much as the original check. What was the amount of the check? (Note: 1 dollar = 100 cents.)

Answer on next page

By George White

Let x be the number of dollars in the check, and y be the number of cents.

Then 100y + x − 50 = 3(100x + y).Therefore 97y − 299x = 50.

A standard solution to this type of linear Diophantine equation uses Euclid's algorithm.

The steps of the Euclidean algorithm for calculating the greatest common divisor (gcd) of 97 and 299 are as follows:

299 = 3 × 97 + 897 = 12 × 8 + 1

This shows that gcd(97,299) = 1.To solve 97y − 299x = gcd(97,299) = 1, we can proceed

backwards, retracing the steps of the algorithm as follows:1 = 97 − 8 × 12 = 97 − (299 − 3 × 97) × 12 = 37 × 97 − 12 × 299

Therefore a solution to 97y − 299x = 1 is y = 37, x = 12.Hence a solution to 97y − 299x = 50 is y = 50 × 37 = 1850, x = 50

× 12 = 600.It can be shown that all integer solutions of 97y − 299x = 50 are

of the form y = 1850 + 299k, x = 600 + 97k, where k is any integer.

In this case, because x and y must be between 0 and 99, we choose k = −6.

This gives y = 56, x = 18.So the check was for $18.56.

By George White

Christiaan Huygens• Christiaan Huygens was born on 14 April 1629, the second child of the poet and statesman

Constantijn Huygens and his wife, Suzanna van Baerle. Christiaan was taught by his father and by specially appointed tutors. When he was eight, a certain Abraham Mirkenius, was hired, whose main task was to teach the brothers Latin, the international language of learning. He also studied geography, prosody, logic, Greek, French, and Italian, while learning to play the lute, viola, and clavichord. When he was fourteen, he became interested in drawing and mechanics. He taught himself to copy printed pictures and built little models of devices he read about. The next year, Christiaan began formal lessons in dancing and horseback riding. At this time, a mathematics tutor, Jan Jansz. Stampioen was hired for Christiaan and his brother Constantijn.

• On 11 May 1645, Christiaan and his brother Constantijn inscribed their names in the student rolls of the University of Leiden. At that time, universities generally offered higher degrees in only three subjects, Law, Theology, and Medicine. The boys father wanted them to study Law, so that they would be able to continue the family tradition of high government service. After two years at Leiden, Christiaan was transferred by his father this time with his younger brother, Lodewijk to the new Illustrious School at Breda, which had just been founded by the Prince of Orange (Frederick Henry), and of which his father was one of the trustees. Here, Christiaan continued his legal studies from March 1647 to August 1649. In 1655, Christiaan went on a voyage to Paris, accompanied by his younger brother Lodewijk and two of their cousins. In those days, such a journey was a customary way for young men of well-to-do families to round off their education.

• In 1656-57, he invented the pendulum clock. At the time, he published only a brief description; a more exhaustive treatment came much later. In 1669 he became so ill that people were worried that he might die. In order to recuperate, he returned to his family in The Hague, where he remained from September 1670 until June 1671. When, in 1681, illness threatened his life for a second time, he again returned to The Hague. For the rest of his life, Huygens remained in the Netherlands, an internationally famous scientist. He continued his research and publications to the end, living off the wealth of his family. After 1687 there was talk now and then of marriage, but Huygens never took that step. In 1695 Huygens health deteriorated rapidly. On 9 July of that year, after having drawn up a will, he passed away. He left his papers to the University of Leiden, where they remain to date. His instruments and telescope lenses remained in the possession of the Huygens family until 1754 when the collection was broken up at a public auction.

Roxana Hayward Vivian• Roxana Hayward Vivian was born in Hyde Park, Boston,

Massachusetts on December 9, 1871. She entered Wellesley College in 1890, graduating in 1894 with a B.A. degree after majoring in Greek and Mathematics. In 1898, Vivian began graduate studies at the University of Pennsylvania as a holder of the Alumnae Fellowship for Women. In 1901 she became the first woman to receive a Ph.D. in mathematics from the University of Pennsylvania.

• Vivian returned to Wellesley College in 1901 as an instructor in mathematics. Vivian was the first member of the Wellesley mathematics department to have a doctorate. She was promoted to associate professor in 1908 and to full professor in 1918. During her twenty-six year career at Wellesley, Vivian had several leaves of absence. From 1913-1914 she was a lecturer in statistics for the University Extension in Boston. During 1913-1915 she also served as the financial secretary for the Women's Educational and Industrial Union of Boston while teaching only one course at Wellesley. In addition to her teaching in the mathematics department, she served as the director of the Graduate Department of Hygiene and Physical Education at Wellesley from 1918 to 1921. This may have been due to the decrease in need of mathematics instructors after Wellesley dropped the requirement in mathematics several years earlier. In a letter to Professor Helen Owens in 1937, however, Vivian wrote:

• "Taught for one year at Wellesley after my delightful year at Cornell, and then was practically forced to resign from my full professorship in mathematics after twenty-six years of teaching at Wellesley. It was, as happens so often, a case of academic jealousy and politics."

• The year after leaving Wellesley, Vivian held a temporary position in mathematics at a private school in Vassalboro, Maine.

Answers:1. 902. 1323. 2850

Math Cartoon

Galileo Galilei

• • Jacob grim 3/19/10• Galileo Galilei 15 February 1564[4] – 8 January 1642)[1][5] was

an Italian physicist, mathematician, astronomer, and philosopher who played a major role in the Scientific Revolution. His achievements include improvements to the telescope and consequent astronomical observations, and support for Copernican's. Galileo has been called the "father of modern observational astronomy the "father of modern physics,"[7] the "father of science,"[7] and "the Father of Modern Science."[8] Stephen Hawking says, "Galileo, perhaps more than any other single person, was responsible for the birth of modern science."[9]

• The motion of uniformly accelerated objects, taught in nearly all high school and introductory college physics courses, was studied by Galileo as the subject of kinematics. His contributions to observational astronomy include the telescopic confirmation of the phases of Venus, the discovery of the four largest satellites of Jupiter (named the Galilean moons in his honour), and the observation and analysis of sunspots

Math and science

• Earth is the planet we live on and the one with water and life as we know it. It is the third largest planet of the nine that orbit the sun. The planets provide a lot of interesting numbers for measurement and computation. We will first examine the distance and size of the planets. Then we will study weight and age if we were to travel to different planets. The main purpose of this page is to learn scientific notation.

• How far are the planets from the Sun?• Planets• Distance from Sun in km • Approx. diameter in km• Mercury• 5.8 x 107

• 4, 840• Venus• 1.03 x 108 • 12, 200• Earth• 1.55 x 108 • 12, 756• Mars• 2.28 x 108

• 6, 787• Jupiter• 7.78 x 108

• 142, 200• Saturn• 1.427 x 109

• 120, 600• Uranus• 2.87 x 109

• 51, 300• Neptune• 4.497 x 109

• 49, 100• Pluto• 5.9 x 109

• 2, 300• Light travels at 300,000 km/second. How much time will it take to send a radio wave from Pluto to the Sun. (assume radio waves

travel at the speed of light).• 5,900,000,000 / 300,000 = 19,666.7 seconds / 60

= 327.8 minutes / 60= 5.46 hours

puzzle

• Why should you never mention the number 288 in front of anyone?

• • Answer Because it is too

gross (2 x 144 - two gross).

Math articles

Women in mathematicsThere are many women known for their contributions to

mathematics. The woman in mathematics that I chose was Suzan Rosa Benedict. Suzan was born in Norwalk, Ohio in 1873. She received her B.A. degree in 1895 from Smith College with a major in chemistry and a minor in mathematics, German, and physics.

Suzan taught high school mathematics in Norwalk from 1895 to 1905 while also working as a real estate agent. She then entered Columbia University, receiving her master's degree in the history of mathematics in 1906. In the same year she started teaching mathematics at Smith College and where she remained for the rest of her professional career.

Suzan continued her graduate studies while teaching, and in 1914 she became the first woman to receive a PhD in mathematics from the University of Michigan. At Smith College Suzan continued her research in the history of mathematics, publishing papers in the Mathematics Teacher the American Mathematical Monthly. Through her efforts the Smith College library developed a large collection of rare books on the history of mathematics. She was promoted to the rank of Professor in 1921. Benedict was also a charter member of the Mathematical Association of America, founded in 1915.

Benedict retired from Smith in February, 1942.She died from a heart attack two months later. Her friendliness was not confined to the College. To her an acquaintance was a friend and people of all sorts and conditions in the town felt that they knew her and will miss her.

By : Christina

Math ArticlesBiographical sketch of a great mathematician

Annie Dale Biddle was born in Hanford, California in 1885. She was the youngest child of Samuel E. Biddle and A. A. Biddle. Annie received her B.A degree from the University of California in 1908.In 1911 she became the first women to receive a PhD in mathematics at the University of California at Berkeley.

Annie was an instructor in mathematics at the University of Washington in 1911-1912. On October 7, 1912 she married Wilhelm Samuel Andrews. They had a daughter, born in 1913, and a son, born in 1919. Annie Andrews was an instructor in mathematics at the University of California during various years between 1915 and 1932. During 1922-23 she taught Mathematical Theory of Investment, Plane Analytic Geometry and Differential Calculus, Solid Analytic Geometry, Integral Calculus, and Infinite Series, College Algebra, and Introduction to Projective Geometry. She was dismissed from her teaching position when the mathematics department was reorganized in 1993.

Also in March, 1933, she presented a research paper on "The space quartic of the second kind by synthetic methods" at a meeting of the American Mathematical Society in Palo Alto. The abstract for the talk was published in the AMS Bulletin. After a two year illness, Andrews died on April 14, 1940, survived by her husband and two children. During the last four years of her life she took an active interest in public affairs and charitable work in addition to her mathematical research.

By: Christina Rockwell

Math Cartoons

Math Challenge Problems

Helen has 3 inches of hair cut off each time she goes to the hair salon. If n equals the length of hair before she cuts it and c equals the length of hair after she cuts it, which equation would you use to find the length of Helen's hair after she visit the hair salon?a) n = 3 - c       c) c = n - 3b) c = 3 - n       d) n = c – 3

Math PuzzlesAnswer Key:Math puzzle:

And We Iz Dizzone!