Link Software Programming - 000003 Computer Science and History

000003 Computer Science & History

1700 B.C. (Estimate)

The Phoenicians who lived in the land that is roughly Lebanon now used the Phonetic alphabet. The Greek language evolved from the phonetic alphabet. And the Latin language evolved from the Greek language.

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700 B.C. (Estimate)

The Etruscan Alphabet was modeled on the Greek alphabet. The Greek alphabet developed into the Latin alphabet. Then the Latin alphabet developed into the Western Languages: English, French, German, etc. The Greeks did not have a number for “zero”, neither did the Romans.

In our current time, numbers can be classified into:

01. Natural Numbers which are positive integers not including zero.

02. Whole Numbers which include Natural Numbers and the zero. In other words Whole Numbers include zero and positive integers.

03. Integer Numbers and Float Numbers. Integer Numbers include zero and positive integers and negative integers.

04. Rational Numbers and Irrational Numbers. Rational Numbers are numbers that can be represented in the form of a ratio of two integers. Irrational are numbers that cannot be represented in the form of a ratio of two integers. Examples of irrational numbers are: the square root of 2 and PI.

05. Positive Numbers and Negative Numbers.

06. Even Numbers and Odd Numbers.

07. Terminating Numbers and Non-Terminating Numbers.

08. Composite Numbers and Prime Numbers. Composite Numbers are numbers that can be factored into numbers other than 1 and the number itself. Prime Numbers are Integer Numbers that are A. Equal to or larger than 2 AND that are B. Only divisible by 1 and the number itself.

Prime Numbers can be further divided into:

08.1.1. Co-Prime Numbers.

08.1.2. Triplet Prime Numbers.

08.1.3. Mersenne Numbers.

08.1.4. Regular Prime Numbers.

08.1.5. Pseudoprime Numbers.

09. Set Numbers. Set Numbers can be sub-classified into:

09.01 Empty Set.

09.02 Singleton Set.

09.03 Finite Set.

09.04 Infinite Set.

09.05 Equal Sets.

09.06 Equivalent Sets.

09.07 Universal Set.

09.08 Subset.

09.09 Proper Subet.

09.10 Superset.

09.11 Proper Superset.

09.12 Power Set.

10. Radical Numbers are numbers with an absolute exponent less than 1.

11. Harshad Numbers.

12. Graham Numbers.

13. Ten-Based Numbers (Decimal Numbers); Two-Based Numbers (Binary Numbers); Eight-Based Numbers (Octal Numbers); Sixteen-Based Numbers (Hexadecimal Numbers).

The Ten-Based Numbers (Decimal Numbers) usually use the ten Arabic Numbers (0, 1, 2, 3, 4, 5, 6, 7, 8, 9).

The Two-Based Numbers (Binary Numbers) usually use the two Arabic Numbers (0, 1).

The Eight-Based Numbers (Octal Numbers) usually use the eight Arabic Numbers (0, 1, 2, 3, 4, 5, 6, 7).

The Sixteen-Based Numbers (Hexadecimal Numbers) usually use the ten Arabic Numbers (0, 1, 2, 3, 4, 5, 6, 7, 8, 9) and the six Latin letters (A, B, C, D, E, F)

14. Real Numbers and Imaginary Numbers and Complex Numbers.

15. Special Numbers.

16. Carmichael Numbers.

17. Transcendental Numbers.

18. Perfect Numbers.

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600 B.C. (Estimate)

Tarqunius Pricus introduced the Roman Republican Calendar which was a lunar calendar of 355 days.

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580 B.C. (Estimate)

Birth of the Greek philosopher and mathematician Pythagoras.

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500 B.C. (Estimate)

Introduction of a Chinese mathematical assertion that stated:

if (n) | ( ( (2) ^ (n-1) ) - 1), then n must be a prime number.

In other words:

if modulus ( ( ( (2) ^ (n-1) ) - 1) , (n) ) = 0, then n must be a prime number.

In the current programming languages, this assertion can be stated in Python as follows:

if ( ( (2) ** (n-1) ) - 1) % (n) == 0:

print (“The number n is a prime number”)

else:

print (“The number n is not a prime number”)

And it can be stated in Microsoft Excel as follows:

=if(mod(( ( (2)^(n1-1))-1),(n1))=0,"The number n is a prime number","The number n is not a prime number")

This assertion was proven to be false in 1820 A.D. This is even though this assertion is true to all numbers less than and including 340. The number 340 includes 271 composite numbers and 69 prime numbers). However this assertion is not true for n = 341. This is since (341) | ( ( (2) ^ (341-1) ) - 1) and 341 is NOT a prime as 341 can be factored into 11 * 31.

However there was another Chinese assertion going back to the same time of 500 B.C. that stated:

if n is prime, then (n) | ( ( (2) ^ (n-1) ) - 1)

This other assertion is true. Fermat Little Theory that came in 1640 was a generalization of this other Chines assertion.

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500 B.C. (Estimate)

Death of the Greek philosopher and mathematician Pythagoras at the age of 80 (Estimate). He contended that Truth in its very depth is mathematical, and that numbers are the foundation of everything.

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500 B.C. (Estimate)

Invention of the Abacus.

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428 B.C. (Estimate)

Birth of Plato, the Greek philosopher. He was a student of Socrates. Plato wrote the story of the Atlantis which was not proven to be either a pure fiction or based on reality. One of his sayings was: “Access to power must be confined to those who are not in love with it.”

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400 B.C. (Estimate)

Hippocrates wrote two books on health: “Regimen in Health” and “Regimen” in which he advocated walking. Hippocrates is the physician after which the “Hippocratic Oath” was named. Hippocrates was influenced by the writings of the Greek wrestling and boxing instructor Herodicus in 400 B.C. (Estimate).

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384 B.C. (Estimate)

Birth of the Greek philosopher Aristotle, who was a student of Plato. One of Aristotle’s sayings was: “Beauty is a greater recommendation than any letter of introduction.”

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377 B.C. (Estimate)

Death of Hippocrates at the age of 83 (Estimate).

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350 B.C. (Estimate)

The Greek Mathematician Menachmus was the first to put a theory on conic sections which included ellipse, parabola, and hyperbola.

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347 B.C. (Estimate)

Death of Plato at the age of 81 (Estimate).

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320 B.C. (Estimate)

The Greek Euclid (Evcleidis) wrote a book on the conic sections.

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275 B.C. (Estimate)

Death of the Greek mathematician Euclid (Evcleidis) at the age of 55.

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267 B.C. (Estimate)

Death of the Egyptian historian Manetho at the age of 67 (Estimate).

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212 B.C. (Estimate)

Death of the Greek mathematician Archimedes at the age of 75 (Estimate). He was educated in Alexandria, Egypt. He discovered one the basic principles of fluid mechanics. He also estimated that the number of grains of dust on earth is ( (10^8) * (10^8) ) ^ (10^8) which is 1 followed by 80,0 million million zeros. He used the Aristarchus estimation of the universe size.

In our current time, the terms that are used to describe the integral part of a number left to the decimal point include:

Tens: 01 Zero

Hundreds: 02 Zeros

Thousands: 03 Zeros

Millions: 06 Zeros

Billions: 09 Zeros

Trillions: 12 Zeros

Quadrillions: 15 Zeros

Quintillion: 18 Zeros

Sextillion: 21 Zeros

Septillion: 24 Zeros

Octillion: 27 Zeros

And in our current time, the terms that are used to describe the fractional part of a number right to the decimal point include:

(The fractional part of a number right to the decimal point sometimes is referred to as mantissa)

Deci: 1 / 01 Zero

Centi: 1 / 02 Zeros

Milli: 1 / 03 Zeros

Micro: 1 / 06 Zeros

Nano: 1 / 09 Zeros

Pico: 1 / 12 Zeros

Femto: 1 / 15 Zeros

Atto: 1 / 18 Zeros

Zepto: 1 / 21 Zeros

Zocto: 1 / 24 Zeros

Epsilon is used in mathematics to represent a positive infinitesimal quantity

EPSILON is used in programming languages as a name of a constant of infinitesimal quantity. This helps overcome the shortcomings of the binary system in some calculations. And thus we avoid logical errors resulting from these shortcomings of the binary system. One of the shortcomings of the binary system is its inexact representation of some of the fractions in the decimal system.

Epsilon is the fifth letter of the 24 letters of the Greek Alphabet:

01 Alpha

02 Beta

03 Chi

04 Delta

05 Epsilon

06 Eta

07 Gamma

08 Iota

09 Kappa

10 Lambda

11 Mu

12 Nu

13 Omega

14 Omicron

15 Phi

16 Pi

17 Psi

18 Rho

19 Sigma

20 Tau

21 Theta

22 Upsilon

23 Xi

24 Zeta

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180 B.C. (Estimate)

The Greek mathematician Zenodorus proofed that the area of any polygon is smaller than the area of a circle of an equal perimeter. This principle was called “The Perimetric Problem”.

Polygons can be classified in different ways:

Classification A:

01. Complex Polygon.

02. Simple Polygon.

Classification B:

01. Concave Polygon.

02. Convex Polygon.

Classification C:

01. Irregular Polygon.

02. Regular Polygon.

Classification D (By the number of sides):

01. 03 sides Triangle.

01.01. Equilateral Triangle.

01.02. Isosceles Triangle.

01.03. Scalene Triangle.

01.04. Acute Triangle.

01.05. Obtuse Triangle.

01.06. Right Triangle.

02. 04 sides Quadrilateral (or Tetragon). Quadrilateral means “four sides”. Quad means four. Lateral means side.

02.01. Irregular Quadrilateral.

02.02. Regular Quadrilateral.

02.02.01. Kite.

02.02.02. Parallelogram.

02.02.03. Rectangle.

02.02.04. Rhombus.

02.02.05. Square.

02.02.06. Trapezoid (or Trapezium).

02.03. 05 sides Pentagon.

02.04. 06 sides Hexagon.

02.05. 07 sides Heptagon.

02.06. 08 sides Octagon.

02.07. 09 sides Nonagon (or Enneagon).

02.08. 10 sides Decagon.

02.09. 11 sides Hendecagon (or Undecagon).

02.10. 12 sides Dodecagon.

02.11. 13 sides Triskaidecagon (13-gon).

02.12. 14 sides Tetrakaidecagon (14-gon).

02.13. 15 sides Pentadecagon (15-gon).

02.14. 16 sides Hexakaidecagon (16-gon).

02.15. 17 sides Heptadecagon (17-gon).

02.16. 18 sides Octakaidecagon (18-gon).

02.17. 19 sides Enneadecagon (19-gon).

02.18. 20 sides Icosagon (20-gon).

02.19. 30 sides Triacontagon (30-gon).

02.20. 40 sides Tetracontagon (40-gon).

02.21. 50 sides Pentacontagon (50-gon).

02.22. 60 sides Hexacontagon (60-gon).

02.23. 70 sides Heptacontagon (70-gon).

02.24. 80 sides Octacontagon (80-gon).

02.25. 90 sides Enneacontagon (90-gon).

02.26. 100 sides Hectogon (100-gon).

02.27. 1,000 sides Chiliagon (1,000-gon).

02.28. 10,000 sides Myriagon (10,000-gon).

02.29. 1,000,000 sides Megagon (1,000,000-gon).

02.30. 10^100 sides Googolgon (10^100-gon).

02.31. m sides (m-gon). m=infinity:

02.31.01 Circle.

02.31.02 Ellipse.

02.31.03 Sector.

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47 B.C.

The burning of Alexandria Library in Alexandria, Egypt.

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46 B.C.

Julius Caesar (at the age of 54) appoints the Greek astronomer Sosigenes as his advisor. Sosigenes of Alexandria, Egypt who was a reputable Greek astronomer and mathematician. Julius Caesar called on him to bring order to the calendar. The lunar calendar that was introduced in 600 B.C. was abandoned. Then 3 months were inserted in the year 46 B.C. The year was set to be 365 days with an extra day placed between February 23 and February 24 every four years.

The reason for inserting one day every 4 years has been because it takes the sun 365 days, 5 hours, 48 minutes, and 46 seconds to complete one revolution around the earth. Therefore one year is equal to ( (365) days ) + ( (5/24) day ) + ( ( (48) / (60*24) ) day ) + ( ( (46) / (60*60*24) ) day ) = ( (365) day ) + ( (0.2083333333) day ) + ( (0.0333333333) day ) + ( (0.0005324074) day ) = (365.242199074) day.

The 365.25-day year was very close to 365.242199074. This calendar was known as the Julian Calendar. This year (46 B.C.) was called the last year of confusion and the leap year introduced. But the Romans were still confused and they errored by making the last year of the 4-year period as the first year of the following period. This mistake went uncorrected for 36 years until 8 B.C. In 8 B.C. the emperor Augustus ordered the cancelling of three leap days. Then in 4 A.D. the Julian Calendar was corrected again. Finally, in 1582 A.D. the last correction was made to the calendar that is still use in our current time.

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8 B.C.

The emperor Augustus ordered the cancelling of three leap days from the Julian Calendar.

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4 B.C.

The Julian calendar was corrected for the second time.

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40 A.D.

Birth of the Roman engineer Sextus Julius Frontinus.

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103 A.D.

Death of the Roman engineer Sextus Julius Forntinus at the age of 63.

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200 A.D.

The Greek physician Gallen who was the physician to the gladiators wrote a book titled “On Hygine” about exercise. Gallen was influenced by Hippocrates. Gallen was influential for centuries and was studied in European Medical Schools in the 13th century.

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370 A.D.

Birth of the mathematician Hypatia in Alexandria, Egypt.

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598 A.D.

Birth of the Hindu mathematician Brahmagupte who found many of the rules of permutations and combinations.

The 4 main permutation and combination formulas that are in use in our current time are:

Permutation (n, r) without repetition {n>=r} = (n)! / (n-r)!

Permutation (n, r) with repetition = (n) ^ (r)

Combination (n, r) without repetition {n>=r} = (n)! / ( (n-r)! * (r)! )!

Combination (n, r) with repetition = (n+r-1)! / ( (n-1)! * (r)! )

Factorial is represented by the symbol “!”. Power is represented by the symbol “^”. Multiplication is represented by the symbol “*”. Division is represented by the symbol “/”. Mathematical Precedence is represented by parenthesis.

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628 A.D.

The Hindu mathematician Brahmagupta at the age of 30 introduced the notion of negative numbers. He stated that:

"-" + "-" = "-"

"-" - "-" = "-" or "+"

"-" * "-" = "+"

"-" / "-" = "+ "

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630 A.D.

The Hindu astronomer Brahmagupta wrote about astronomy with a clear understanding of the notion of negative numbers. Later, the French Mathematician Blaise Pascal thought that numbers less than zero could not exist.

Also, the German Mathematician Gottfried Leibniz thought that negative numbers could lead to absurd conclusions and misconceptions. We know now that Blaise Pascal and Gottfried Leibniz were wrong.

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780 A.D.

Birth of Mathematician Mohamed (Muhammad) Ibn Musa Al-Khwarizmi (Al-Khowarizmi).

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825 A.D.

The mathematician Mohamed (Muhammad) Ibn Musa Al-Khwarizmi (Al-Khowarizmi) at the age of 45 wrote a book which was the oldest known writing using a fully developed numeration system. The Arabic numbers (0, 1, 2, 3, 4, 5, 6, 7, 8, 9) are still in use today after they have replaced other number systems including the Roman numbers. Al-Khwarizmi has been known as the father of algebra.

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850 A.D.

Death of Mohamed (Muhammad) Ibn Musa Al-Khwarizmi (Al-Khowarizmi) at the age of 70.

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935 A.D.

King Harald Blatand (which means Harold Blue Tooth) king of Denmark and Norway from 935 and 936 respectively, to 940. He was known for his unification of previously warring tribes from Denmark, Norway, and Sweden. The technology later called “Blue Tooth” was named after him. The term “Blue Tooth” was intended to unify technologies like computers and cell phones. The Blue Tooth logo combines the Nordic runes for H and B. It was said that the story of king Harald Blatand as a unified force was more or less based on the novel “Long Ships” by Frans Gunnar Bengtsson. “Long Ships” was a Swedish best-selling Vicking-inspired novel. In April 1998, Intel and Microsoft formed a consortium between themselves and IBM, Ericsson, Nokia, Toshiba, and Puma Technology where the code name Bluetooth was adopted for their proposed open specification.

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1202 A.D.

The Italian mathematician Leonardo Fibonacci (Leonardo of Pisa) wrote “Liber Abaci”. Fibonacci was inspired by the Muslim mathematician Mohamed (Muhammad) Ibn Musa Al-Khwarizmi (Al-Khowarizmi). Al-Khwarizmi had died some 352 before Fibonacci wrote “Liber Abaci”. “Liber Abaci” dealt with arithmetic and algebra. Fibonacci also wrote “Practica Geometriae”.

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May 27, 1332 A.D.

Birth of the Muslim sociologist Ibn-Khaldoon (Abo-Zeed Abd-El-Rahman Ibn-Mohamed Ibn-Khaldoon).

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March 19, 1406 A.D.

Death of Ibn-Khaldoon at the age of 73.

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1545 A.D.

The Italian Girolamo Cardano wrote “Ars Magna” that included the usage of negative numbers. He also was a physician and gave an early clinical description of typhoid.

This was some 915 years after the Hindu astronomer Brahmagupta in 630 A.D. wrote about astronomy with a clear understanding of the notion of negative numbers.

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1572 A.D.

Ugo Buoncompagni, a former teacher of law at the University of Bologna became Pope Gregory XIII. In this year, the calendar was 10 days short, the vernal equinox fell on March 11 instead of its proper date March 21.

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February 24, 1582 A.D.

Some 10 years after becoming the Pope, Gregory XIII acting on the advice of two renowned astronomers, issued a papal edict directing that the Julian Calendar be corrected “to allow the calendar to catch up with the Lord’s time”. The correction was made by making October 4, 1582 be October 15, 1582. The new calendar was called the Gregorian Calendar.

The Gregorian Calendar introduced 29 days in February every 4 years which would be called leap years with the exception of centennial years which would not be leap years unless they are divisible by 400.

Therefore a year would be a leap year when:

Modulus (year , 4) = 0 and Modulus (year , 100) <> 0

with the following exception: a year would be a leap year when Modulus (year , 400) = 0

The reason for inserting one day every 4 years and omitting 3 days every 400 years has been because it takes the sun 365 days, 5 hours, 48 minutes, and 46 seconds to complete one revolution around the earth.

Therefore one year is equal to ( (365) days ) + ( (5/24) day ) + ( ( (48) / (60*24) ) day ) + ( ( (46) / (60*60*24) ) day ) = ( (365) day ) + ( (0.2083333333) day ) + ( (0.0333333333) day ) + ( (0.0005324074) day ) = (365.242199074) day.

The 365.25-day year was very close to 365.242199074.

365.25 days - 365.242199074 days =

0.007800926 day per year difference =

0.187222224 hour per year difference =

11.23333344 minutes per year difference =

674.0000064 seconds per year difference

0.007800926 * 400 = 3.1203704 day per 400 years

Therefore, this calendar would be off by +0.1203704 day per 400 years

+0.1203704 day per 400 years =

+0.000300926 day per year =

+0.007222224 hour per year =

+0.43333344 minute per year =

+26.0000064 seconds per year

The Gregorian Calendar became known as the New Style and was recognized by nearly all countries of Catholic faith. Protestant countries were more resistant to accept this Gregorian Calendar.

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1584 A.D.

The end of using Latin in business transactions in Oxford University.

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Sunday, March 31, 1596 A.D.

Birth of the French mathematician and philosopher Rene Descartes. He invented the branch of geometry known as Analytical Geometry (Cartesian Geometry).

In our current time, many types of geometry were introduced through history. This includes:

1. Euclidean Geometry

2. Plane Geometry (2-D Geometry)

3. Analytic Geometry (Cartesian Geometry)

4. Descriptive Geometry

5. Solid Geometry

6. Fractal Geometry

7. Differential Geometry

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1601 A.D.

Birth of the French lawyer and mathematician Pierre de Fermat. Fermat came up with a formula to generate prime numbers: Fn = (2 ^ ( 2 ^ n) ) + 1. This formula was later proven to be wrong. It was first proven to be wrong in 1732 by Leonard Euler.

In this year 1601 A.D.:

The French philosopher Rene Descartes was about 5 years old.

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Monday, June 19, 1623 A.D.

Birth of the French mathematician, physicist, and inventor Blaise Pascal.

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1640 A.D.

Fermat at the age of 39 introduced Fermat's Little Theorem (FLT). Fermat's Little Theorem was a generalization of a Chinese assertion in 500 B.C. (Estimate). This Chinese assertion tstated:

if n is prime, then (n) | ( ( (2) ^ (n-1) ) - 1)

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1642 A.D.

Birth of the British mathematician Issac Newton. He was the author of “Philisophiae Naturalis Principia Mathematica” known as “Principa”.

In this year 1642 A.D.:

The French mathematician Pierre de Fermat was 41 years old.

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1642 A.D.

At the age of 18, the French mathematician Blaise Pascal designed and constructed the first working mechanical calculator, “The Pascaline”.

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1646 A.D.

Birth of the German mathematician Gottfreid Wilhelm Leibniz.

In this year 1646 A.D.:

The British mathematician Issac Newton was 4 years old.

The French mathematician Pierre de Fermat was 45 years old.

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Friday, February 11, 1650 A.D.

Death of the French mathematician and philosopher Rene Descartes at the age of 54.

In this year 1650 A.D.:

The French mathematician Pierre de Fermat was 49 years old.

The British mathematician Isaac Newton was 8 years old.

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1655 A.D.

John Wallis introduced the mathematical symbol of infinity in his “Arithmetica Infinitorum”. Yet it was not put in print until 1713 by Jakob Bernoulli.

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Saturday, August 19, 1662 A.D.

Death of the French mathematician, physicist, inventor Blaise Pascal at the age of 39.

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1665 A.D.

Death of the French mathematician and lawyer Pierre de Fermat at the age of 64.

In this year 1665 A.D.:

The British mathematician Isaac Newton was 23 years old.

The German mathematician Gottfreid Wilhelm Leibniz was 19 years old.

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1667 A.D.

Birth of the Swiss scientist Johann Bernoulli.

In this year 1667 A.D.:

The German mathematician Gottfreid Wilhelm Leibniz was 21 years old.

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1684 A.D.

At the age of 38, the German Mathematician Gottfreid Wilhelm Leibniz published his system for calculus. His book was titled “Nova Methodus Pro Maximis et Minimis”. In English, it meant: A New Method for Determining Maxima and Minima.

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1694 A.D.

At the age of 48, the German mathematician Gottfried Wilhelm Leibniz completed the “Step Reckoner”, the first calculator that could perform all four arithmetic operations. This was some 52 years after the French mathematician Blaise Pascal at the age of 18 designed and constructed the first working mechanical calculator, “The Pascaline”.

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1700 A.D.

Protestant Germany accepted the Gregorian Calendar some 118 years after this calendar was introduced in the era of the Pope Gregory XIII.

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1707 A.D.

Birth of the Swiss mathematician Leonhard Euler.

In this year 1707 A.D.:

The German Mathematician: Gottfreid Wilhelm Leibniz was 61 years old.

The British mathematician Isaac Newton was 65 years old.

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1713 A.D.

The Swiss Mathematician Jakob Bernoulli introduced the symbol for infinity in print in his “Ars conjectandi”. It was published by Jakob Bernoulli’s cousin Nikoluas Bernoulli (Nikolaus I).

In this year 1713 A.D.:

The Swiss mathematician Johann Bernoulli was 46 years old.

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1738 A.D.

Daniel Bernoulli introduced the Bernoulli’s Principle that described the behavior of fluids under non-turbulent conditions.

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1748 A.D.

Death of the Swiss mathematician Johann Bernoulli at the age of 81.

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1752 A.D.

Britain accepted the Gregorian Calendar some 169 years after this calendar was introduced in the era of the Pope Gregory XIII.

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1753 A.D.

Sweden accepted the Gregorian Calendar some 170 years after this calendar was introduced in the era of the Pope Gregory XIII.

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1768 A.D.

Birth of the French mathematician Jean Baptiste Joseph Fourier.

In this year 1768 A.D.:

The Swiss Mathematician Leonhard Euler was 61 years old.

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1783 A.D.

Death of the Swiss Mathematician Leonhard Euler at the age of 76.

In this year 1783 A.D.:

The French mathematician Jean Baptiste Joseph Fourier was 15 years old.

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Wednesday, November 28, 1810 A.D.

Birth of the British naval architect William Froude. He was the first to formulate reliable laws for the resistance that water offers to ships. He formulated the hull speed equation and predicting the ship’s stability. Hull Speed in Knots =1.34 * (Length of the Water Line in Feet)^0.5. A boat travelling at a speed more than its hull speed would face drastically more water resistance than the water resistance it would face at speeds below its hull speed.

Froude Number= Speed of the Boat/ the Boat Length.

An example of the application of the Froude Number is the following:

The Norwegian Eirik Veraas Larsen won the gold medal in Athens 2004 in the kayaking (K1-1000 meters) event. His winning time was 3:25.897. Larsen’s average speed would have been 1/(3:25.897/60) kilometer/hour = 17.48447039 kilometer/hour =10.864 346 21 mile/hour. Larsen’s kayak was 17.6 feet long. Thus the hull speed of his kayak = 1.34 * (17.6)^0.5 = 1.34 * 4.13 = 5.53 knots = 6.37 Mile/hour = 10.25 kilometer/hour. Larsen Kayak’s speed exceeded the hull speed by about 70%. He had to face drastic increase in water resistance when his speed exceeded his hull speed of 10.25 kilometer/hour.

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1820 A.D.

It was discovered that the error in the Chinese mathematical assertion going back to 500 B.C. that stated: if n|2^n-1 -1, then n must be prime is false.

This is even though this assertion is true to all numbers less than and including 340. The number 340 includes 271 composite numbers and 69 prime numbers. However this assertion is not true for n = 341. This is since (341) | ( ( (2) ^ (341-1) ) - 1) and 341 is NOT a prime as 341 can be factored into 11 * 31.

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1826 A.D.

The Swiss mathematician Jacob Steiner found the solution for the “Lines in-the-plane Problem”.

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1830 A.D.

Death of the French mathematician Jean Baptiste Joseph Fourier at the age of 62.

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1835 A.D.

Birth of the scientist Auguste Kerckhoffs.

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1838 A.D.

The American inventor Samuel Morse developed the original Morse code.

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1851 A.D.

The Morse code was modified to the International Morse Code. This was some 13 years after the American inventor Samuel Morse developed the original Morse code.

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1876 A.D.

The largest number to be proven prime without the usage of the electronic computer was M127 in Mp= (2^p) - (1) where p is a prime number. The M label was named after Marin Mersenne. Mersenne was a friend of Fermat.

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1877 A.D.

Birth of the British Mathematician G.H. Hardy. He wrote a book titled “A Mathematician Apology”.

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Sunday, May 4, 1879 A.D.

Death of the British naval architect William Froude at the age of 68.

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1880 A.D.

It was proven that F6 was not a prime number in the formula written by Fermat to generate prime numbers: Fn = (2 ^( 2 ^ n) ) + 1. F6 has a prime factor of 274177.

Some 148 years earlier (1732 A.D.), Leonard Euler proved that F5 was not a prime number in Fermat prime number generating formula: Fn = (2 ^( 2 ^ n) ) + 1.

F5 = 4,294,967,297= 641*6700*41

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1883 A.D.

The French mathematician Edouard Lucas invented a puzzle named The Tower of Hanoi. Its solution is Tn= (2^n) – 1.

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Friday, October 19, 1900 A.D.

The German physicist Max Planck submitted to the Berlin Physical Society an important proposal. This proposal stated that the electromagnetic radiation (visible light, infrared radiation, ultraviolet radiation, and the rest of the electromagnetic spectrum) exist as tiny indivisible packets of energy rather than a continuous stream. He later christened these packets “Quanta”. Planck was then a new professor at the University of Berlin. This was the foundation of Quantum Physics as opposed to Classical Physics. From the ideas of Quantum Physics spawned technologies including transistors, lasers, semiconductors, light-emitting diodes, scans, PET scan, and MRI.

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Friday, October 31, 1902 A.D.

Birth of Mathematician Abraham Wald. He established the field of Statistical Sequential Analysis.

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1903 A.D.

Death of the scientist Auguste Kerckhoffs at the age of 68.

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1905 A.D.

It was proven that F7 was not a prime number in the formula written by Fermat to generate prime numbers: Fn = (2 ^( 2 ^ n) ) + 1

This was some 25 years after F6 was proven to be not a prime number in 1880. And it was some 173 years after F5 was proven to be not a prime number in 1732.

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1918 A.D.

U.S.S.R. accepted the Gregorian calendar some 336 years after this calendar was introduced.

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Saturday, March 25, 1922 A.D.

Birth of Stephen Edelston Toulmin in London, U.K. In 1958, he wrote “The Uses of Arguments”. He found theories that dealt with practical issues using moral reasoning. He developed a system to break down any type of arguments and the assumptions that surround it. This influenced philosophy, rhetoric, and computer science.

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1923 A.D.

Greece accepted the Gregorian calendar some 341 years after this calendar was introduced.

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Sunday, August 11, 1946 A.D.

Birth of the mathematician Marilyn vos Savant. She later introduced a solution to the Monty Hall Paradox.

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1947 A.D.

Death of the British Mathematician G.H. Hardy at the age of 70.

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Wednesday, December 13, 1950 A.D.

Death of Mathematician Abraham Wald at the age of 48.

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1953 A.D.

The University of Cambridge established the first computer science degree.

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Tuesday, January 31, 1956 A.D.

Birth of Guido van Rossum who later found the computer programming language: Python.

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August 1959 A.D.

At the age of 32, the mathematician Bernhard Riemann presented a paper to the Berlin Academy titled: “On the Number of the Prime Numbers Less Than a Given Quantity”.

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1962 A.D.

The first computer science degree program in the United States was formed at Purdue University. This was some 9 years after the University of Cambridge established the first computer science degree in 1953. And by the end of the 20th century, some 5.8 % of the engineers in the U.S.A. were graduates of Purdue University.

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1963 A.D.

The establishing of the American Standard Code for Informational Interchange (ASCII). ASCII covered up to 256 digits, letters, and symbols. This was enough to cover the English alphabet and other related digits and symbols. However ASCII was way short to cover the alphabets, digits, and symbols of other languages.

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1971 A.D.

In the formula written by Fermat to generate prime numbers: Fn = (2 ^( 2 ^ n) ) + 1, F7 was factorized in two prime numbers of 17, 22 digits respectively.

This was some 66 years after F7 was proven to be not a prime number. And it was some 91 years after F6 was proven to be not a prime number. And it was some 239 years after F5 was proven to be not a prime number. And it was some 331 years after the French mathematician and lawyer Pierre de Fermat came up with a formula to generate prime numbers: Fn = (2 ^( 2 ^ n) ) + 1.

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1972 A.D.

The first computer engineering degree program in the United States was established at Case Western Reserve University. This was some 10 years after the first computer science degree program in the United States was formed at Purdue University in 1962.And this was some 19 years after the University of Cambridge established the first computer science degree in 1953.

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1981 A.D.

Microsoft released Microsoft Disk Operating System (MS DOS).

In this year 1981:

Guido van Rossum was 24 years old. Some 10 years later, Rossum found the programming language Python.

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1985 A.D.

PNY Technologies Inc. was established.

PNY later described its establishment as follows:

“Established in 1985, PNY Technologies, Inc. delivers a full spectrum of high-quality products for everything in and around the computer. PNY is a leading manufacturer and supplier of computer graphics accelerator cards for consumers and professional graphics boards for professionals, memory upgrade modules, Flash Media and Flash peripherals. PNY products are used by a number of Fortune 500 OEM customers for applications that range from high-end computing and Internet/telecommunications infrastructure equipment to desktop, notebook and network servers. The company's retail product line includes products used in a growing number of consumer electronics devices, such as personal computers, digital cameras and PDA devices. PNY products are now available at major retail outlets, mail order outlets, online retailers, value-added resellers and distribution channels throughout the U.S. and Europe.

Throughout its history, PNY has helped to redefine itself by delivering segmented product lines targeted to specific groups of computer enthusiasts, including the youth market, computer programmers, systems designers, digital animators, engineers, presentation professionals and graphic artists. In tailoring its product lines to these specific consumer groups, PNY has built substantial brand equity, and established meaningful relationships with retailers and consumers alike. The company further supports its dealers and customers with toll-free technical support, a lifetime warranty and an unwavering commitment to customer satisfaction. As a result, PNY has earned its position among the most respected companies in the industry.”

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November 1985 A.D.:

Microsoft released Windows 1.0. This was about 5 years after Microsoft released Microsoft Disk Operating System (MS DOS) in 1981.

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Monday, September 14, 1987 A.D.

Microsoft unveiled Microsoft Works (MS Works) for DOS. This was about 2 years after Microsoft released Microsoft Windows 1.0 in 1985. And this was about 7 years after Microsoft released Microsoft Disk Operating System (MS DOS) in 1981.

Later, Microsoft Works has developed through the years to include a suite including word processor, spread sheet, database, and other software.

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November 1987 A.D.

Microsoft released Windows 2.0. This was about 2 years after Microsoft released Microsoft Windows 1.0 in 1985. And this was about 7 years after Microsoft released Microsoft Disk Operating System (MS DOS) in 1981.

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January 1988 A.D.

Microsoft released Microsoft Windows 2.03.

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1990 A.D.

It was proven that F9 was not a prime number in the formula written by Fermat to generate prime numbers: Fn = (2 ^( 2 ^ n) ) + 1

This was some 19 years after F7 was proven to be not a prime number in 1971. And it was some 110 years after F6 was proven to be not a prime number in 1880. And it was some 258 years after F5 was proven to be not a prime number in1732. And it was some 350 years after the French mathematician and lawyer Pierre de Fermat came up with a formula to generate prime numbers: Fn = (2 ^( 2 ^ n) ) + 1 in 1640.

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1990 A.D.

Microsoft released Microsoft Windows 3.0.

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Sunday, September 9, 1990 A.D.

At the age of 44, Marilyn vos Savant answered in her column a question from a reader about what later became known as the Monty Hall Paradox. Marilyn Savant wrote a column called “Ask Marilyn” in a newspaper called Parade. Marilyn Savant was known for having one of the highest recorded IQ. Marilyn Savant’s response caused protest from her readers. The opposition of Marilyn Savant’s response also came from mathematicians and academicians. Articles and books were written over this problem.

We can design computer programs in different programming languages to simulate the Monty Hall Paradox. These programs simulation prove without a doubt that Marilyn Savant was very much right.

There are numerous functions to generate pseudo random numbers in Python. This helps in simulations to answer questions as the one of the Monty Hall Paradox. These random functions include:

import random

pseudoRandomNumber01=random.random()

pseudoRandomNumber02=random.randint(Integer01,Integer02)

pseudoRandomNumber03=random.uniform(Integer03,Integer04)

pseudoRandomNumber04=random.choice(List01)

pseudoRandomList01=random.choices(List01,k=Integer05)

pseudoRandomList02=random.choices(List02,weights=[Integer07,Integer08,Integer09],k= Integer10)

pseudoRandomList03=random.shuffle(List01)

pseudoRandomList04=random.sample(List01,k= Integer10)

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1992 A.D.

The establishing of the Unicode some 29 years after the establishing of the American Standard Code for Informational Interchange (ASCII) in 1963. Unicode Transformation Format (UTF) replaced ASCII. ASCII covered up to 256 digits, letters, and symbols. UT16 could cover up to 65,536 digits, letters, and symbols. UT32 could cover up to 4,294,967,296 digits, letters, and symbols. Thus Unicode Transformation Format was capable of covering alphabets and symbols of so many languages other than the English language.

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Sunday, March 1, 1992 A.D.

Microsoft released Microsoft Windows 3.1.

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July 1993 A.D.

Microsoft released Microsoft Windows NT. This was about a 1.5 years after Microsoft released Microsoft Windows 3.1.

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