Negative Numbers.

Slides:



Advertisements
Similar presentations
Fermat’s Last Theorem Dr. S. Lawrence ©2005.
Advertisements

What kind of mp3 player do mathematicians use?
BY LAM TRAN The Historical development of number and number systems.
Chapter 2 Reading and Writing Arithmetic Presented by Lucas Mellinger MAT 400.
Math 191: Mathematics and Geometry for Designers Lecture Notes Based on The Book Mathematics in Our World by Allan G. Bluman.
Hawkes Learning Systems: College Algebra
Something Less Than Nothing? Negative Numbers By: Rebecca Krumrine and Kristina Yost.
PRE - ALGEBRA.
The Cubic formula Milan vs. Venice (Cardano and Tartaglia) 1500’s.
IB HL Adrian Sparrow Factor and remainder theorem.
Copyright © Cengage Learning. All rights reserved. 0 Precalculus Review.
College Algebra Fifth Edition James Stewart Lothar Redlin Saleem Watson.
Daniel Blanchette, Christian Landry. 1300BC1300BC Babylonians Solved quadratics of the form x 2 + p = qx.
Chapter 11 Polynomial Functions
MTH070 Elementary Algebra Chapter 1 Review of Real Numbers and Problem Solving Copyright © 2010 by Ron Wallace, all rights reserved.
Exponents, Polynomials, and Polynomial Functions.
5.2 The Integers. Whole Numbers The set of whole numbers contains the set of natural numbers and the number 0. Whole numbers = {0,1,2,3,4,…}
History of the Quadratic Equation Sketch 10
Shapes by the Numbers Coordinate Geometry Sketch 16 Kristina and Jill.
Complex Numbers. Once upon a time… Reals Rationals (Can be written as fractions) Integers (…, -1, -2, 0, 1, 2, …) Whole (0, 1, 2, …) Natural (1, 2, …)
By: Darion Keyes. Nothing is known about Euclid’s life except what the Greek philosopher Proclus said in his reports “summary” of famous Greek mathematicians.
Wednesday, August 19, 2015 We are learning to…add and subtract positive and negative integers with Algebra Tiles.
Rules of Integers. Positive numbers are numbers that are above zero. Negative numbers are numbers below zero.
Chapter 1 Section 6 Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley.
Writing Whole Numbers K. McGivney MAT400
 John was born at Ashford on November 22, 1616  He became interested in mathematics after reading his brother’s arithmetic book and with his help, mastering.
MEDIEVAL AND RENAISSANCE MATHEMATICS BY: Tajana Novak, Andrea Gudelj, Sr đ ana Obradović, Mirna Marković April, 2013.
Hero’s and Brahmagupta’s Formulas Lesson Hero of Alexandria He was an ancient Greek mathematician and engineer who was born in 10 AD. He invented.
Whole Numbers Are the whole numbers with the property of addition a group?
Special Numbers.
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, … -> 0,1, 2, 3, 4, 5, 6, 7, 8, 9, 10, …-> -10, -9, -8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, …->
Chapter 4 Number Theory in Asia The Euclidean Algorithm The Chinese Remainder Theorem Linear Diophantine Equations Pell’s Equation in Brahmagupta Pell’s.
Algebra Introduction & Useful Websites. Origin of Algebra Many say that the Babylonians first developed systems of quadratic equations. This calls for.
Introduction to Algebra
PART 3 THINKING MATHEMATICALLY. 3.1 MATHEMATICS AS AN AXIOMATIC-DEDUCTIVE SYSTEM.
Copyright © Cengage Learning. All rights reserved. Real Numbers and Their Basic Properties 1.
Prerequisites: Fundamental Concepts of Algebra
Extending the Definition of Exponents © Math As A Second Language All Rights Reserved next #10 Taking the Fear out of Math 2 -8.
Exponent Rules Essential Question: How can I simplify and evaluate algebraic equations involving integer exponents?
Mathematicians By: Baylee Maynard.
Precalculus Polynomial & Rational --- Part One V. J. Motto.
Computational Physics PS 587. We are still waiting for the Ph D class to join in… Till then, refresh some concepts in programming (later). Discuss some.
Ch 2.5: The Fundamental Theorem of Algebra
Fundamental Theorem of Algebra and Brouwer’s Fixed Point Theorem (talk at Mahidol University) Wayne Lawton Department of Mathematics National University.
Integers Done by Greshma,Anshul,Sanchitha, Srivats,Khushi and Rishabh.
Operations with Integers
Integers.
Quadratic Equations Starting with the Chinese in 2000 BC.
Adding and Subtracting Signed Integers
11.3 The Number e. The Number e  John Napier is famous for computing tables on logarithms.  In a 1618 book of logarithm tables, William Oughtred (an.
4.6 Solving Quadratic Equations by Factoring BobsMathClass.Com Copyright © 2010 All Rights Reserved. 1 Solving Quadratic Equations by Factoring The Multiplication.
Zero: Infinity’s Twin By Travis Mackoy. Life Without Zero oZero was not needed in primitive societies oMathematics was originally “one” or “many” o30,000.
The original people who began to have ideas about the number zero were the Babylonians, though the actual number was designed by the Mayans and then finally.
Chapter 7: Rational Algebraic Functions Section 7-11: Variation Functions.
Linear Thinking Chapter 9: Solving First Degree Equations.
Algebra 1 Chapter 2 Section : Solving One-Step Equations An equation is a mathematical statement that two expressions are equal. A solution of an.
College Algebra Sixth Edition James Stewart Lothar Redlin Saleem Watson.
TRANSLATING Word phrases to algebraic expressions.
Number Systems Integers Positive & Negative Numbers.
Algebra An Introduction. The History of Algebra The history of algebra began In Ancient Egypt and Babylon where basic equations were first solved. Our.
The Number Zero By zee oddo.
The Rise of Islamic Mathematics 8 th – 13 th Century.
What is an Equation  An equation is an expression with an ‘equal’ sign and another expression.  EXAMPLE:  x + 5 = 4  2x – 6 = 13  There is a Left.
The History Of Calculus
Week 1 Real Numbers and Their Properties (Section 1.6, 1.7, 1.8)
Irrational Numbers.

LEAVING CERT ALGEBRA SUMMARY OF THE SECTIONS IN L.C. ALGEBRA NOTES
Classical Indian Science
Adding and Subtracting Polynomials
Presentation transcript:

Negative Numbers

Chinese Mathematics 200 BCE: Chinese Rod System Commercial calculations Red rods cancelled black rods Amount Sold: Positive Amount Spent: Negative

Negative Numbers Brahmagupta – 7th Century Mathematician 1st wrote of negative numbers Zero already had a value Developed rules for negative numbers Developed the Integers we know

Arithmetic rules with Integers Brahmagupta’s work Translation to modern day A debt minus zero is a debt A fortune minus zero is a fortune Zero minus zero is zero A debt subtracted from zero is a fortune A fortune subtracted from zero is a debt Negative – 0 = negative Positive – 0 = positive 0 – 0 = 0 0 – negative = positive 0 – positive = negative

Arithmetic rules with Integers – cont’d Brahmagupta’s work A product of zero multiplied by a debt or fortune is zero The product of zero multiplied by zero is zero The product or quotient of two fortunes is a fortune The product or quotient of two debts is a fortune The product or quotient of a debt and a fortune is a debt The product or quotient of a fortune and a debt is a debt YOUR TURN – Write an example that illustrates each rule on your white board

Negative numbers in greece Ignored and Neglected by Greeks On your white board: Mathematics in Greece established through Geometry 300 CE: Diophantus wrote Arithmetica 4 = 4x + 20 “Absurd result” Why would problems arising from Geometry cause Greeks to ignore negative numbers?

Arabian mathematics Also ignored negatives Al-Khwarizami’s Algebra book – 780 CE 6 forms of linears and quadratics Acknowledged Brahmagupta Heaviily influenced by the Greeks Called Negative Results “meaningless”

Arabian mathematics – cont’d His contribution to math Al-Samawal (1130 – 1180 CE) Produced statements regarding algebra “If we subtract a positive number from an empty power, the same negative number remains” Also had statements about products and quotients al-Samawal is said to have been developing algebra of polynomials Which one of the statements to the left suggests this? What do you think he was trying to say?

European mathematics 15th century Arabs brought negatives to Europe Translated ancient Islamic and Byzantine texts Spurred solutions to quadratics and cubics

European mathematics Luca Pacioli (1445 – 1517) Italian Summa Double Entry Book-Keeping John Wallis ( 1616-1703) English Invented Number Line

European mathematics 1758: Francis Maseres British “ (negative numbers) darken the very whole doctrines of the equations and made dark the things which are in their nature excessively obvious and simple”

European mathematics 1770: Euler Swiss “Since negative numbers may be considered as debts ... We say that negative numbers are less that nothing. Thus, when a man has nothing of his own, and owes 50 crowns, it is certain that he has 50 crowns less than nothing; though if any were to make a present of 50 crowns to pay his debt, he would still have nothing, though really richer than before.”

SOURCES History of Negative Numbers: http://nrich.maths.org/5961 Brahmagupta: http://www.storyofmathematics.com/indian_brahmagupta.html The History of Mathematics: http://www.math.tamu.edu/~dallen/masters/hist_frame.htm Negative Numbers: http://people.cst.cmich.edu/piate1kl/mth_553_f07/negative_numbers_small.pdf MacTutor History of Mathematics: http://www-history.mcs.st-and.ac.uk

Feedback: Privacy Policy Feedback
Do Not Sell My Personal Information
About project: SlidePlayer Terms of Service

© 2025 SlidePlayer.com. Inc. All rights reserved.