Computers and Applied Mathematics Antonia santamaría y alejandro silva

Introduction:

Since the first computer was created, the mathematics have advanced exponentially. The technology has been a positive discovery in many aspects, one of them, the development of new skills in math, for example, the calculators.

Blaise Pascal (1623-1662):

-Was a French writer, mathematician, physicist, Christian philosopher and inventor.

-Invented the Pascal's calculator or the mechanical calculator (1642-1644) that could perform the basic operations of arithmetic (add, subtract and keep the answers). It could only had eight figures at a time.

-Created the Probability Theory

-He also made the Pascal's Triangle that showed the binomial coefficients.

"Each number is the sum of the two directly above it."

Gottfried Wilhelm Leibniz (1646-1716):

-German polymath and philosopher

-He added multiplication and division to Pascal's Calculator creating the Pin Wheel Calculator in 1685.

-This calculator was smaller and cheaper than the Pascaline and it could perform the four basic operations (add, subtract, divide and multiply)

-This new invention led to the Aritmometer in 1820 by Thomas de Colmar that could perform big numbers operations.

-Gottfried improved the binary system which is the base of all digital computers.

-The binary numbers are just the zero (0) and the one (1). This two can combine in all possibly combinations (examples: 10110, 100011101, 111010, etc) and represent all the real numbers.

The (1) acts like "positive", "open" or "yes" and the (0) acts like "close", "negative" or "no"

The image above shows how the number 12 is represented with the binary system. As you can see the one's are placed in the column of 2^3 = 8 and 2^2 = 4 and the zero's are placed on the rest of the columns. The columns where the one's are placed are summed 8+4 and the result is 12.

This system can also add, subtract, multiply and divide binary numbers. Here are some explanations:

Allan Turing (1912-1954) :

-Mathematician and scientific of computation

-He is known as the father of modern computation

-In 1936 he wrote the Church-Turing thesis that formalised the concepts of algorithms and computation

-His best known work was made during World War II deciphering instructions of the German navy to the submarines.

-Turing designed processes and machines capable of performing combinatorial calculations much faster than any human.

-Later he committed suicide with a poisoned apple. This is why Apple's logo is a bitten apple.

A Cheerful Fact: The Pythagorean Theorem

-Created by Phythagoras, a philosopher that founded the religious movement Pythagoreanism.

-The Pythagorean Theorem proves that the two sides or legs, that make up the 90º angle of a triangle, when they are to the second power and are added together, are the length of the third side of the triangle or the hypotenuse.

Summary

Thanks to all of this events we can do any operation we want. Also we have access to computers that give us all the information we need. Without this men we wouldn't be able to develop the math skills we have today.

Work Cited:

"History of Computers and Computing, Mechanical calculators, Pioneers, Blaise Pascal." History of Computers and Computing, Mechanical calculators, Pioneers, Blaise Pascal. N.p., n.d. Web. 02 Apr. 2017. <http://history-computer.com/MechanicalCalculators/Pioneers/Pascal.html>.

Bogomolny, Alexander. "History of the Binary System." Interactive Mathematics Miscellany and Puzzles. N.p., n.d. Web. 02 Apr. 2017. <http://www.cut-the-knot.org/do_you_know/BinaryHistory.shtml>.

"GEO-LOCATED INTERACTIVE TIMELINES WITH A SOCIAL TWIST." Create Free Interactive Timelines – Stories Displayed on Maps | myHistro. N.p., n.d. Web. 02 Apr. 2017. <http://www.myhistro.com/dashboard>.

"Alan Turing." Britannica School. N.p., n.d. Web. 02 Apr. 2017. <http://school.eb.com/levels/high/article/Alan-Turing/73839>.

"Pascaline." Britannica School. N.p., n.d. Web. 02 Apr. 2017. <http://school.eb.com/levels/high/article/Pascal/443512>.

"Gottfried Wilhelm Leibniz." GALE-STUDENT RESOURCES IN CONTENT. N.p., 2006. Web. 2 Apr. 2017. <http://ic.galegroup.com/ic/suic/BiographiesDetailsPage/BiographiesDetailsWindow?disableHighlighting=false&displayGroupName=Biographies&currPage=&scanId=&query=&source=&prodId=SUIC&search_within_results=&p=SUIC&mode=view&catId=&u=colnoga&limiter=&display-query=&displayGroups=&contentModules=&action=e&sortBy=&documentId=GALE%7CK2641500129&windowstate=normal&activityType=&failOverType=&commentary=>.

Singh, Simon. Fermat's Last Theorem. Great Britain: Fourth State, 1997. Print.

Credits:

Created with images by TCB - "abacus slide rule computer" • HamuD - "laptop math desk" • Hans - "pythagoras mathematics formal" • Wokandapix - "calculator math mathematics"

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