Wednesday, 28 December 2016

REAL LIFE APPLICATION OF MATHEMATICS IN BASKETBALL


The angle at which the ball is thrown is determined as the angle made by the extension of the player's arms and a perpendicular line starting from the player's hips.


The Mathematics in Basketball

The math in basketball involves a wide range of math topics. Kids can practice geometry, percentages and even basic mathematical operations while playing or watching a game of basketball.
§  Geometry in basketball
Whether they realize it or not, basketball players make use of many geometric concepts while playing a game. The most basic of these ideas is in the dimensions of the basketball court. The diameter of the hoop (18 in), the diameter of the ball (9.4 in), the width of the court (50 ft) and the length from the three point line to the hoop (19 ft) are all standard measures that must be adhered to in any basketball court. Knowing these measurements is useful for kids who would like to practice basketball at home without access to a full-fledged basketball court.
The path the basketball will take once it’s shot comes down to the angle at which it is shot, the force applied and the height of the player’s arms. When shooting from behind the free throw line, a smaller angle is necessary to get the ball through the hoop. However, when making a field throw, a larger angle is called for. When a defender is trying to block the shot, a higher shot is necessary. In this case, the elbows should be as close to the face as possible.
Understanding arcs will help determine how best to shoot the ball. Basketball players understand that throwing the ball right at the basket will not help it go into the hoop. On the other hand, shooting the ball in an arc will increase its chances of falling through the hoop. Getting the arc right is important to ensure that the ball does not fall in the wrong place.
The best height to dribble can also be determined mathematically. When standing in one place, dribble from a lower height to maintain better control of the ball. When running, dribbling from the height of your hips will allow you to move faster. To pass the ball while dribbling, use straighter angles to pass the ball along a greater distance.
Understanding geometry is also important for good defense. This will help predict the player’s moves, and also determine how to face the player. Facing the player directly will give the player greater space to move on either side. However, facing the player at an angle will curb his freedom. Mathematics can also be used to decide how to stand while going on defense. The more you bend your knees, the quicker you can move.  Utilizing geometry, math in basketball plays a crucial role in the actual playing of the sport.
§  Statistics in basketball
Statistics is essential for analyzing a game of basketball. For players, statistics can be used to determine individual strengths and weaknesses. For spectators, statistics is used to determine the value of players and analyze the performance of an individual or the entire team. Percentages are a common way of comparing players’ performances. It is used to get values like the rebound rate, which is the percentage of missed shots a player rebounds while on the court. Statistics is also used to rank a player based on the number of shots, steals and assists made during a game. Averages are used to get values like the points per game average, and ratios are used to get values like the turnover to assist ratio.
§  Addition and Subtraction in Basketball
For young basketball fans, math in basketball is a great opportunity to practice simple skills like counting, addition and subtraction. Young kids can add up the points made in every shot to get the team’s total score. Kids can also be asked to use subtraction to determine how many points a team will need to catch up with the leading team, or to win the game.


Reference:
wikipedia

HISTORY OF SRINIVASA RAMANUJAN



ALSO LISTED IN
FAMOUS AS
Mathematician
NATIONALITY
BORN ON
22 December 1887 AD
BIRTHDAY
22nd December    Famous 22nd December Birthdays
CENTURY
DIED AT AGE
32
SUN SIGN
Sagittarius    Sagittarius Men
BORN IN
Erode
DIED ON
26 April 1920 AD
PLACE OF DEATH
Chetput
PERSONALITY TYPE
Ambitious, Confident
GROUPING OF PEOPLE
Illiterates
CAUSE OF DEATH
Illness
CHARACTER TRAITS
Intelligent
FATHER
K. Srinivasa Iyengar
MOTHER
Komalat Ammal
SIBLINGS
Sadagopan
SPOUSE/PARTNER:
Janaki Ammal
EDUCATION
Town Higher Secondary School
1906 - Government Arts College
Kumbakonam
Pachaiyappa's College
1920 - Trinity College
Cambridge
1919 - University of Cambridge
1916 - University of Cambridge
University of Madras











Srinivasa Ramanujan was an Indian mathematician who made significant contributions to mathematical analysis, number theory, and continued fractions. What made his achievements really extraordinary was the fact that he received almost no formal training in pure mathematics and started working on his own mathematical research in isolation. Born into a humble family in southern India, he began displaying signs of his brilliance at a young age. He excelled in mathematics as a school student, and mastered a book on advanced trigonometry written by S. L. Loney by the time he was 13. While in his mid-teens, he was introduced to the book ‘A Synopsis of Elementary Results in Pure and Applied Mathematics’ which played an instrumental role in awakening his mathematical genius. By the time he was in his late-teens, he had already investigated the Bernoulli numbers and had calculated the Euler–Mascheroni constant up to 15 decimal places. He was, however, so consumed by mathematics that he was unable to focus on any other subject in college and thus could not complete his degree. After years of struggling, he was able to publish his first paper in the ‘Journal of the Indian Mathematical Society’ which helped him gain recognition. He moved to England and began working with the renowned mathematician G. H. Hardy. Their partnership, though productive, was short-lived as Ramanujan died of an illness at the age of just 32.
Childhood & Early Life
·   Srinivasa Ramanujan was born on 22 December 1887 in Erode, Madras Presidency, to K. Srinivasa Iyengar and his wife Komalatammal. His family was a humble one and his father worked as a clerk in a sari shop. His mother gave birth to several children after Ramanujan, but none of them survived infancy.
·    Ramanujan contracted smallpox in 1889 but recovered from the potentially fatal disease. While a young child, he spent considerable time in his maternal grandparents’ home.
·    He started his schooling in 1892. Initially he did not like school though he soon started excelling in his studies, especially mathematics.
·    After passing out of Kangayan Primary School, he enrolled at Town Higher Secondary School in 1897. He soon discovered a book on advanced trigonometry written by S. L. Loney which he mastered by the time he was 13. He proved to be brilliant student and won several merit certificates and academic awards.
·    In 1903, he got his hands on a book called ‘A Synopsis of Elementary Results in Pure and Applied Mathematics’ by G.S. Carr which was a collection of 5000 theorems. He was thoroughly fascinated by the book and spent months studying it in detail. This book is credited to have awakened the mathematical genius in him.
·    By the time he was 17, he had independently developed and investigated the Bernoulli numbers and had calculated the Euler–Mascheroni constant up to 15 decimal places. He was now no longer interested in any other subject, and totally immersed himself in the study of mathematics only.
·    He graduated from Town Higher Secondary School in 1904 and was awarded the K. Ranganatha Rao prize for mathematics by the school's headmaster, Krishnaswami Iyer.
·    He went to the Government Arts College, Kumbakonam, on scholarship. However, he was so preoccupied with mathematics that he could not focus on any other subject, and failed in most of them. Due to this, his scholarship was revoked.
·    He later enrolled at Pachaiyappa's College in Madras where again he excelled in mathematics, but performed poorly in other subjects. He failed to clear his Fellow of Arts exam in December 1906 and again a year later. Then he left college without a degree and continued to pursue independent research in mathematics.
Later Years
·    After dropping out of college, he struggled to make a living and lived in poverty for a while. He also suffered from poor health and had to undergo a surgery in 1910. After recuperating, he continued his search for a job.
·    He tutored some college students while desperately searching for a clerical position in Madras. Finally he had a meeting with deputy collector V. Ramaswamy Aiyer, who had recently founded the Indian Mathematical Society. Impressed by the young man’s works, Aiyer sent him with letters of introduction to R. Ramachandra Rao, the district collector for Nellore and the secretary of the Indian Mathematical Society.
·    Rao, though initially skeptical of the young man’s abilities soon changed his mind after Ramanujan discussed elliptic integrals, hypergeometric series, and his theory of divergent series with him. Rao agreed to help him get a job and also promised to financially fund his research.
·    Ramanujan got a clerical post with the Madras Port Trust, and continued his research with the financial help from Rao. His first paper, a 17-page work on Bernoulli numbers, was published with the help of Ramaswamy Aiyer, in the ‘Journal of the Indian Mathematical Society’ in 1911.
·    The publication of his paper helped him gain attention for his works, and soon he was popular among the mathematical fraternity in India. Wishing to further explore research in mathematics, Ramanujan began a correspondence with the acclaimed English mathematician, Godfrey H. Hardy, in 1913.
·    Hardy was very impressed with Ramanujan’s works and helped him get a special scholarship from the University of Madras and a grant from Trinity College, Cambridge. Thus Ramanujan travelled to England in 1914 and worked alongside Hardy who mentored and collaborated with the young Indian.
·    In spite of having almost no formal training in mathematics, Ramanujan’s knowledge of mathematics was astonishing. Even though he had no knowledge of the modern developments in the subject, he effortlessly worked out the Riemann series, the elliptic integrals, hypergeometric series, and the functional equations of the zeta function.
·    However, his lack of formal training also meant that he had no knowledge of doubly periodic functions, the classical theory of quadratic forms, or Cauchy’s theorem. Also, several of his theorems on the theory of prime numbers were wrong.
·    In England, he finally got the opportunity to interact with other gifted mathematicians like his mentor, Hardy, and made several further advances, especially in the partition of numbers. His papers were published in European journals, and he was awarded a Bachelor of Science degree by research in March 1916 for his work on highly composite numbers. His brilliant career was however cut short by his untimely death.
Major Works
·    Considered to be a mathematical genius, Srinivasa Ramanujan, was regarded at par with the likes of Leonhard Euler and Carl Jacobi. Along with Hardy, he studied the partition function P(n) extensively and gave a non-convergent asymptotic series that permits exact computation of the number of partitions of an integer. Their work led to the development of a new method for finding asymptotic formulae, called the circle method.
Awards & Achievements
·    He was elected a Fellow of the Royal Society in 1918, as one of the youngest Fellows in the history of the Royal Society. He was elected "for his investigation in Elliptic functions and the Theory of Numbers."
·    The same year, he was also elected a Fellow of Trinity College—the first Indian to be so honored.
Personal Life & Legacy
·    He was married to a ten-year-old girl named Janakiammal in July 1909 when he was in his early 20s. The marriage was arranged by his mother. The couple did not have any children, and it is possible that the marriage was never consummated.
·    Ramanujan suffered from various health problems throughout his life. His health declined considerably while he was living in England as the climatic conditions did not suit him. Also, he was a vegetarian who found it extremely difficult to obtain nutritious vegetarian food in England.
·    He was diagnosed with tuberculosis and a severe vitamin deficiency during the late 1910s and returned home to Madras in 1919. He never fully recovered and breathed his last on 26 April 1920, aged just 32.
·    His birthday, 22 December, is celebrated as 'State IT Day' in his home state of Tamil Nadu. On the 125th anniversary of his birth, India declared his birthday as 'National Mathematics Day.'
Top 10 Facts You Did Not Know About Ramanujan
·    Ramanujan was a lonely child in school as his peers could never understand him.
·    He hailed from a poor family and used a slate instead of paper to jot down the results of his derivations.
·    He did not receive any formal training in pure mathematics!
·    He lost his scholarship to study at Government Arts College as he was so obsessed with mathematics that he failed to clear other subjects.
·    Ramanujan did not possess a college degree.
·    He wrote to several prominent mathematicians, but most of them did not even respond as they dismissed him as a crank due to the lack of sophistication in his works.
·    He became a victim of racism in England.
·    The number 1729 is called Hardy-Ramanujan number in his honor following an incident regarding a taxi with this number.
·    A biographical film in Tamil based on Ramanujan’s life was released in 2014.
·    Google honored him on his 125th birth anniversary by replacing its logo with a doodle on its home page.

Refer from wikipedia



REAL LIFE APPLICATIONS OF TRIGONOMETRY



Trigonometry simply means calculations with triangles (that’s where the tri comes from). It is a study of relationships in mathematics involving lengths, heights and angles of different triangles. The field emerged during the 3rd century BC, from applications of geometry to astronomical studies. Trigonometry spreads its applications into various fields such as architects, surveyors, astronauts, physicists, engineers and even crime scene investigators.
Now before going to the details of its applications, let’s answer a question have you ever wondered what field of science first used trigonometry?
The immediate answer expected would be mathematics but it doesn’t stop there even physics uses a lot of concepts of trigonometry. Another answer According to Morris Kline, in his book named- Mathematical Thought from Ancient to Modern Times, proclaimed that ‘trigonometry was first developed in connection with astronomy, with applications to navigation and construction of calendars. This was around 2000 years ago. Geometry is much older, and trigonometry is built upon geometry’. However, the origins of trigonometry can be traced to the civilizations of ancient Egypt, Mesopotamia and India more than 4000 years ago.
Trigonometry can be used to measure the height of a building or mountains:
 Iyou know the distance from where you observe the building and the angle of elevation you can easily find the height of the building. Similarly, if you have the value of one side and the angle of depression from the top of the building you can find and another side in the triangle, all you need to know is one side and angle of the triangle.

Trigonometry in marine engineering:


In marine engineering trigonometry is used to build and navigate marine vessels. To be more specific trigonometry is used to design the Marine ramp, which is a sloping surface to connect lower and higher level areas, it can be a slope or even a staircase depending on its application.

Trigonometry used in navigation:
Trigonometry is used to set directions such as the north south east west, it tells you what direction to take with the compass to get on a straight direction. It is used in navigation in order to pinpoint a location. It is also used to find the distance of the shore from a point in the sea. It is also used to see the horizon.

Trigonometry in construction:


In construction we need trigonometry to calculate the following:
  • Measuring fields, lots and areas;
  • Making walls parallel and perpendicular;
  • Installing ceramic tiles;
  • Roof inclination;
  • The height of the building, the width length etc. and the many other such things where it becomes necessary to use trigonometry.
Architects use trigonometry to calculate structural load, roof slopes, ground surfaces and many other aspects, including sun shading and light angles.