- 1. SIGNIFICANCE OF NUMBERS IN LIFE AND NATURE Dr. Farhana Shaheen Yanbu University College
- 3. Unit -09 Does Everyone Need Math? • What Exactly is Mathematics? • Arithmetic? • Algebra? • Geometry? • Trigonometry? • Are you good at math? • Problems with MATH? 3
- 4. Math THE QUEEN OF ALL SCIENCES
- 5. Mathematics: Comes from the Greek word “Mathema” meaning “Science, Knowledge, or Learning” • The study of Figures and Numbers. • The Science that deals with Numbers, Quantities, Shapes, Patterns, Measurement and the concepts related to them.
- 6. MATH IS THE BUILDING BLOCK OF ALL SCIENCES • It is the building block for everything in our daily lives, including mobile devices, architecture (ancient and modern), art, money, engineering, and even sports. 6
- 7. BRANCHES OF MATHEMATICS • ARITHMETIC: uses numbers with operations of +, -, *, / • ALGEBRA: Uses letters and symbols to represent numbers and amounts. • GEOMETRY: Study of shapes • TRIGONOMETRY: Study of angles and sides of triangles. 7
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- 10. Maths is ALL AROUND US • In everything we do.
- 11. Life Without Maths- is NOTHING 11
- 12. • Guess? • Where? In this room? 12
- 13. • In shopping… In baking, cooking- • As percentage? As Ratio? • Or as Fractions? 13
- 15. Tally Marks: Numerals used for counting 15
- 16. Who invented number systems? • The Mayans according to historians are first who invented the number systems 3400 BC. 16
- 17. • After them independently Egyptians around 3100 BC invented their numeral system. 17
- 19. How to memorize? Use Mnemonics- MEMORY TECHNIQUE I VIEW X-RAY I =1 V = 5 X=10 LUCKY CATS DRINK MILK L=50 C = 100 D = 500 M = 1000 19
- 20. The Arabic Numerals • The Arabic Numerals are the numbers we use today! Note that each Arabic Numeral has the number of angles equal to the number it represents. 20
- 21. How were numbers invented? 21
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- 25. How do you find Maths, to be?
- 26. How many of you think…..? • ??? OR
- 27. Why is Math HARD?
- 28. Are YOU afraid of Maths? • Why are so many of our students so mathematically afraid? • Why do so many of our children appear so distant and so disinterested in so many aspects of classroom mathematics? • What are the major reasons?
- 29. What do you find difficult? 29
- 30. Learning Math Issues: Many students claim that there are too many mathematics formulas to remember. This can be a contributing factor to students' lack of interest in classroom mathematics.
- 31. NOTHING IS DIFFICULT--- • ------ ONLY, IF YOU KNOW HOW/// 31
- 32. Do you feel like---?/?
- 33. And….How many of you think…..?
- 34. Do you? 34
- 35. What do we need to do? To Study MATHS- and get Good Grades
- 36. KEEP PRACTICING--- • NEVER GIVE UP- • BE CONFIDENT- • WE LEARN FROM OUR MISTAKES • REMEMBER---
- 37. NEVER start your morning without taking Breakfast. Do you know WHY?
- 38. While studying, esp. Maths- • Especially a piece of DARK CHOCOLATE-
- 39. Say Bye to Calculator- Go for mental Maths • Say Nooooo… • To Calculator/ • Mental Math sharpens your mind
- 40. Talking Calculator for Kids • http://pbskids.org/cyberchase/math- games/calculator/ 40
- 41. Let’s see how fast we are in mental Maths- ;) • Think of a number- ??? • Double it--- • Add 6 to it • Divide it into half • Deduct your number- • And- the Answer is ???
- 43. • If 1 = 5 • 2 = 10 • 3 = 15 • 4 = 20 • Then…. • 5 = ?
- 44. MATH PUZZLE Let’s try solving this- 44
- 45. Guess the missing numbers?
- 52. STORY OF NUMBERS • The story of numbers begins with Natural numbers = {1, 2, 3, 4, 5, ……} initiated by counting, Whole Numbers, Integers, Real Numbers, and ends up to the set of Complex Numbers, the largest existing numbers, comprising of Real and Imaginary numbers (x+iy, where , x, y are real). 52
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- 54. Special Subsets of Integers • Set of Integers Z = {….-3,-2,-1, 0, 1, 2,..} a subset of Real Numbers, has many specific subsets like: Even Numbers: 0, 2, 4, 6, 8, … Odd Numbers: 1, 3, 5, 7, 9, … Prime Numbers, Composite Numbers, Fibonacci Numbers, Lucas Numbers, etc. 54
- 55. What are Prime Numbers • Numbers which have only two divisors (factors), 1 and the number itself. • A prime number can be divided, without a remainder, only by itself and by 1. • For example, the only factors of 17 are 17 and 1. • 2, 3, 5, 7, 11, 13, 17, 19, 23, … are all primes. • A prime number must be a whole number greater than 1. 55
- 56. Composite Numbers • A number which has divisors other than 1 and itself are called Composite Numbers. • Example: 15= 1x3x5 • A composite number is defined as any number, greater than 1, that is not prime. • Every composite number can be written as a product of primes. For example: 54= 2.3.3.3 Note: Except for 0 and 1, a number is either a prime number or a composite number. 56
- 57. Prime factorization of number 48 using Tree Diagram 57
- 58. Properties of Primes • Number 1 is neither a prime nor a composite number. • Number 2 is the ONLY Even prime number and the smallest prime too. • All other prime numbers are odd. • All prime numbers are positive numbers. • Prime numbers are infinite. 58
- 59. How to find Prime Numbers List of Prime Numbers... 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, ... • We can use Sieve of Eratosthenes to find Prime Numbers. • To find all primes numbers less than 100, write all numbers starting from 2. • Start with 2, and cancel all multiples of 2. • Then start with 3 and cancel all multiples of 3. • Similarly go for 5, 7, 11. The remaining numbers are all Primes. 59
- 61. Sieve of Eratosthenes • The sieve of Eratosthenes is one of the most efficient ways to find all of the smaller primes (below 10 million or so). It is named after Eratosthenes of Cyrene, an ancient Greek mathematician; although none of his works have survived, the sieve was described and attributed to Eratosthenes in the Introduction to Arithmetic by Nicomachus. 61
- 62. How many prime numbers are there? • The table below gives you an indication of how many prime numbers there are in all numbers. For example in the range 0 to 10,000,000 there are 664,579 prime numbers. 62 Range 0 to ? No of Primes % Prime 10 4 40.0% 100 25 25.0% 1,000 168 16.8% 10,000 1,229 12.3% 100,000 9,592 9.6% 1,000,000 78,498 7.8% 10,000,000 664,579 6.6% 100,000,000 5,761,455 5.8% 1,000,000,000 50,847,534 5.1% 10,000,000,000 455,052,511 4.6%
- 63. Primality • The property of being prime is called primality. Verifying the primality of a given number n can be done by trial division. The simplest trial division method tests whether n is a multiple of an integer m between 2 and . If n is a multiple of any of these integers then it is a composite number, and so not prime; if it is not a multiple of any of these integers then it is prime. • Is the number 2311 a Prime? n 63
- 64. The prime number 73,939,133 • The prime number 73,939,133 has a very strange property. If you keep removing a digit from the right hand end of the number, each of the remaining numbers is also prime. It's the largest number known with this property. Take a look: 73,939,133 and 73,939,13 and73,939,1 and 73,93 9 and 7,393 and 739 and 73 and 7 are all prime! 64
- 65. Where do we find these numbers in our daily life? • In our body? • In nature? • In our daily routine? • In the Islamic rituals that we follow? • Or…In Cryptography??? • (Greek kryptos hidden, graphein to write) 65
- 66. Let us see where we find Prime numbers in human body… Are Prime numbers important in our life? 66
- 67. Look at your face: • One head, but two parts of brain • One nose but two nostrils • 2 eyes, 2 ears, 2 cheeks • One mouth but 2 lips 67
- 68. Count your hands, feet, fingers and toes 68
- 69. 2 hands with 5 fingers each 2 feet with5 toes each 69
- 70. • You have ... • 2 hands each of which has • 5 fingers, each of which has • 3 parts separated by • 2 knuckles • Believe it or not, there are 19 bones in each of your hands. • Is this just a coincidence??? Look at your own hand: 70
- 71. There are three things involved in body movement: 1. The Brain 2. Muscles 3. Skeleton. • 1. The brain sends messages to the muscle to let it know it’s time for work. • 2. Muscles contract • 3. Pulls bones attached to them. 71
- 72. Number of bones in leg • 30 in one leg. (excluding the hip) 1- femur (thigh bone) 1- patella (knee cap) 1- tibia (shin) 1- fibula 7- tarsals (ankle bones) 5- metatarsals (foot bones) 14- bones of the toes • (all except the great toe have 3 bones) 72
- 73. Number of Ribs in Human Body • 12 pairs of ribs in human body: 7 are directly connected to the Sternum,(center part) 3 are connected through cartilage 2 are floating and not connected. 73
- 74. Size of Ribs • Twelve pairs of flexible, arch like ribs form the lateral portions of the thoracic cage. They increase in length from the first to the seventh and then decrease again from the eighth to the twelfth. (first 7 increasing and last 5 decreasing) 74
- 75. 29 bones in Skull and 29 in Spine • There are 29 bones in the human skull. The cranium has 8; the face has 15 (including the lower jaw); the ears have 6. There are 29 bones in spinal cord. 75
- 76. Fore and hind legs of quadrupeds are different 76
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- 79. Number 3 79
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- 83. Drink water in three breaks • Water should be drunk in three breaths, that is one should breathe three times outside the drinking vessel one is drinking from. This habit has a salutary impact on one's character and helps one avoid doing things in haste. • Anas, may Allah be pleased with him, reported: The Messenger of Allah, sallallaahu ‘alayhi wa sallam, used to breathe three times in the course of a drink (he used to drink in three gulps). 83
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- 85. 5 Pillars of Islam • The Qur'an presents them as a framework for worship and a sign of commitment to the faith. They are: • (1) The shahada (Kalma), • (2) Daily prayers (salat), • (3) Alms giving (zakāt), • (4) Fasting during Ramadan (sawm) • (5) The pilgrimage to Makkah (Hajj) at least once in a lifetime. 85
- 86. 5 times prayers 5 times prayers: Fajr, Zohar, Asar, Maghrib, Isha • We recite Subhan Rabbiyal Azeem (3 times/ 7 times) and Subhana Rabbiyal Aala (3 times/ 7 times) • Total number of Fardh Prayers = 17 (prime#) 86
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- 88. Reciting Adhkaar- 3,7 or 11 times • Most of the Adhkaar that we recite daily, morning or night, or even after each prayer are in Prime numbers. • For example, reciting Allah-o-Akbar and Astaghferullah 3 times after each Fardh Prayers; • Allah humma ajirna minanna’r 7 times in morning and evening. 88
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- 90. • 90 Violet; Indigo; Blue; Green; Yellow; Orange; Red. 7 Colours in Rainbow
- 91. • 7 days in a week • 7 notes in musical scale 91
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- 95. About Seven Skies in Quran • Seven skies is mentioned a lot in the Quran. What is meant by those skies? “And We have made, above you seven tracts; and We are never unmindful of (Our) Creation.” • In seven verses, the number of the skies is mentioned as “seven”; in two of those verses it is stated that the seven skies are in the form of “layers”. (al-Mulk, 67/3; Nuh, 71/15) “Do you not consider how Allah has created seven heavens in layers” (Surah Nuh 71:15) 95
- 96. 7 Heavens: The atmosphere has 7 layers • Today, it is known that the world's atmosphere consists of different layers that lie on top of each other. Based on the criteria of chemical contents or air temperature, the definitions made have determined the atmosphere of the earth as seven layers. As mentioned in Qur'an (67:3) “He Who created the seven heavens in layer”. 96
- 97. • The statement of "seven heavens" is repeated seven times in Holy Quran. • "The creation of the heavens (khalq as- samawat)" is also repeated seven times. • 7 doors of hell as mentioned in Quran. 97
- 98. 7 Seas The Seven Seas as referenced in Medieval Arabian literature: The Persian Gulf ("Sea of Fars") The Gulf of Khambhat ("Sea of Larwi") Bay of Bengal ("Sea of Harkand”) The Strait of Malacca ("Sea of Kalah”) The Singapore Strait ("Sea of Salahit”) The Gulf of Thailand ("Sea of Kardanj”), and The South China Sea ("Sea of Sanji”). 98
- 99. • Al-Quran- • Surat Luqman 31 • Verse 27, Part 21] 99
- 100. البحار سبعة ، العالم بحار • The "Arabian seven seas" البحار سبعة ، العالم بحارmust also have considered other important seas nearby which were navigated by Arabian and Phoenician seafarers: • the Adriatic Sea • the Arabian Sea • the Black Sea • the Caspian Sea • the Indian Ocean • the Mediterranean Sea • the Red Sea 100
- 101. 7 Oceans 101
- 102. Feast of the Seven Fishes • The Feast of the Seven Fishes is an Italian Christmas celebration. Today, it is a feast that typically consists of seven different seafood dishes. However, some Italian-American families have been known to celebrate with nine, eleven or thirteen different seafood dishes. This celebration commemorates the wait for the midnight birth of the baby Jesus. It is unclear when the term "Feast of the Seven Fishes" was popularized. 102
- 103. • Some people believe that the feast is named for the Seven hills of Rome that surround the city. • 103
- 104. Seven hills of Rome • Tradition holds that the seven hills were first occupied by small settlements and not grouped or recognized as a city called Rome. 104
- 105. H Haft Sheen (7 S- Food) • NOU ROUZ the Persian New Year is the only scientific New Year celebrated in the world today. Nou Rouz is symbolized by the Nou Rouz Table with (haft) seven items with S. • Some call it Haft (seven) Seen and decorate their table with seven items whose names start with the letter “Seen” in Persian. All these items have a positive philosophic meaning. Others use seven items that start with the letter “SHeen”. Still others use seven trays (seenie) and put a variety of items. 105
- 106. Age of Reason- 7 • Around the age of 7, children enter the period of late childhood also called the “age of reason”. This reasonable age, represents the beginning of a new stage of logic and understanding of the surrounding world. This is also the time when their morality begins. 106
- 107. The Age of Seven, (Plus or Minus One). • "It is not until the age of 7, give or take a year or so, that your child's conscience begins to mature enough to guide his/her actions. It's been called the 'Age of Reason,' since these children have a newly internalized sense of right and wrong. They are no longer focused simply on not getting caught or displeasing adults. 107
- 108. • The Messenger of Allah (PBUH) said: ’Command your children to pray when they become seven years old, and enforce them for it (if they refuse to pray) when they become eleven years old.’ • The Messenger of Allah (PBUH) guided the believers to encourage their children to start offering their prayers regularly when they reach seven years of age so that the children form a habit of offering their prayers unto their Lord from a very early age. 108
- 109. • There are many hypotheses for what the number "7" represents. Seven is the most repeated number in the Bible and appears over 700 times. 109
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- 111. Ablution (Wudu) has 7 steps • 1.Pour water over hands and wash them thrice • 2. Rinse mouth thrice • 3.Wash nose by putting water in it and then blowing it out • 4.Then wash face thrice • 5. Wash forearms up to the elbows thrice • 6. Pass wet hands over head, both ears and back side of neck • 7. Wash feet up to the ankles thrice 111
- 112. Prostrating to Allah • Seven parts of our body touch the ground… • Head (Forehead & nose) • Both hands • Both knees • Both feet 112
- 113. During Umrah Tawaf Ka’bah: The circumfering of the Ka'bah 7 times: • 7 rounds of Sai’ 113
- 114. 7 Requirements of Hajj • (If one neglects a requirement he must compensate for it with a ransom (fidyah) an animal sacrificed in Makkah. • Assuming Ihram from the Meeqat • Staying in Arafaat until the sun has set • Staying in Muzdalifah • Staying in Mina on the nights preceding days of Tashreeq • Stoning the pillars (Rami) • Shaving or cutting the hair • The farewell Tawaf (Al-wada) 114
- 115. Stoning of the Pillars • (On 10th of ZilHajj): • Upon reaching Mina, hajjis hasten to stone the large pillar (Jamratul Aqabah) ONLY, with 7 pebbles (throwing one by one), saying “Allahu Akbar” with each pebble thrown (7 times in total). 115
- 116. What to Sacrifice on Eid-ul- Adha? • Generally, slaughter of goats, sheep, rams, cows, and camels is offered. • It is permissible for seven persons to share the sacrifice of a cow or a camel on the condition that no one’s share is less than one seventh and their intention is to offer Qurbani (sacrifice). 116
- 117. Ayyam al-Tashreeq • 11th , 12th, 13th of Zilhajj (Days of Drying Meat) • During these 3 days, (Ayyam at-Tashreeq), the pilgrims stone the 3 pillars, from the time period between after zawaal (sun at highest point- no shadow) until the night. They stone all the 3 Jamarats, for which they need 21 (7x3)pebbles per day. • Method: Throw 7 stones (one by one), saying Allahu Akbar each time: first to the small (Jamratul Sughra), then the medium (Jamratul Wusta), and finally, the large (Jamratul Aqabah) pillar. 117
- 118. Hadith about eating 7 Ajwa dates daily: • Sa’ad told of hearing Allah’s Messenger say, “He who has a morning meal of seven ‘ajwa dates will not suffer harm that day through toxins or magic.” (Bukhari, Hadith 5327 and Muslim, Hadith 3814) 118
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- 120. People of Cave (Ashaab e Kahaf) • They were 3, and 4th was the dog • They were 5, and 6th was the dog • They were 7, and 8th was the dog (as narrated in Quran) 120
- 121. Cicada's mysterious link with primes • I read an article a while back about Cicada's(a type of insect) link with prime numbers, pretty cool how they use prime numbers for their survival. • Reference: ”Mathematicians explore cicada's mysterious link with primes” 121
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- 123. • Cicada's are insects which hibernate underground and emerge every 13 or 17 years to mate and die (while the newborn cicadas head underground to repeat the process). Some people have speculated that the 13/17-year hibernation is the result of evolutionary pressures. 123
- 124. • If cicadas hibernated for X years and had a predator which underwent similar multi- year hibernations, say for Y years, then the cicadas would get eaten if Y divided X. So by "choosing" prime numbers, they made their predators much less likely to wake up at the right time. I guess we have so much to learn from insects as well. 124
- 125. Number 19 in Quran • The Qur'an consists of 114 (19 x 6) Suras. • Another mathematical miracle of the Qur'an is the manner in which the number 19 is numerologically encoded in verses. This number is stressed in the words of the Qur'an: "There are nineteen (angels) in charge of it." (Qur'an, 74:30), and is encoded in various places in the Book. 125
- 126. NUMBER 19 in Quran • The first Sura to be revealed, Surat al-'Alaq, consists of 19 verses and 285 (19 x 15) letters. • A total of 113 Suras in the Qur'an start with Bismillah. Sura not to start with one is the ninth, Surat at-Tawba. Surat an-Naml is the only Sura to have two times Bismillah. One of these is at the beginning and the other in verse 30. Counting from Surat at-Tawba, which does not begin with Bismillah, Surat an-Naml follows 19 Suras on. 126
- 127. NUMBER 19 in Quran • The sum of all the occurrences of the name "Allah" in all the verses whose numbers are multiples of 19 (i.e., verses 19, 38, 57, 76, etc.) is 133, or 19 x 7. • The word "Rahman" (All-Merciful) appears 57 (19 x 3) times in the Qur'an. 127
- 128. • The verse “Which of your Lord’s marvels can you deny” has been repeated 31 times in Surah Al-Rahman which is a prime number. The sum of all the verses numbers where it is repeated, again gives a prime number 1433, and adding these digits gives again 1+4+3+3=11, a prime. 128
- 129. Prime Numbers in Cryptography • You can search for the importance and significance of Prime numbers in Cryptography, the art of sending secret messages, the establishment of a technical system used in maintaining the secrecy of electronic communications. 129
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- 131. Cryptography: How it works? • A cryptographer starts with plain text such as "ATTACKATDAWN" and produces cipher text such as "OTMMGKLHDTIR." This is encryption. Decryption is the reverse: it produces plain text from cipher text. • Large primes are used in this process of encryption and decryption. 131
- 132. • Also the very fundamental concept of prime numbers lies at the very heart of all our online purchases and our banking transactions. 132
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- 134. • They are used extensively in cryptography. For example, there is an approx. 15 digit number on your sim card. It is the product of two prime numbers. Which are both very large numbers. Each one of those number identifies the user and other the carrier location. So their factoring is impossible. This way the 15 digit number ,even if shown publicly cannot disclose any information to hackers. 134
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- 137. • …because:, Seven Ate (eight) Nine- 137
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