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Diophantus was an Alexandrian Hellenistic mathematician which is also known as the father of algebra. He was the author of a series of books called Arithmetica that solved hundreds of algebraic equations, approximately five centuries after Euclid’s era.
See the fact file below for more information on the Diophantus or alternatively, you can download our 22-page Diophantus worksheet pack to utilise within the classroom or home environment.
Key Facts & Information
- Diophantus flourished in the Greco-Roman city of Alexandria in Egypt during the Roman era in the third century AD, presumably from between AD 200 and 214 to 284 or 298.
- Just like the other educated people in the Eastern Mediterranean at that time, he was also a Greek speaker.
- Little is known about his life, even what he looked like.
- The dates of his birth and death are uncertain.
- Diophantus has been described by historians as either Greek, non-Greek, Hellenized Egyptian, Hellenized Babylonian, Jewish, or Chaldean.
- Most of the things we know about the life of Diophantus come from a word puzzle reputed to be his epitaph.
- Presumably, it was written by a friend who knew his life story and who wished to give him a fittingly algebraic memorial.
- The epitaph was created by the Greek author Metrodorus who recorded it in his anthology of puzzles in about the 6th century.
HISTORY OF ARITHMETICA BEFORE DIOPHANTUS
- Diophantus was the author of the influential series of books called the “Arithmetica”. The Arithmetica is a collection of algebraic problems that greatly influenced the subsequent development of number theory.
- Algebra has a lengthy history. From 2000–1600 BC, the Babylonians produced rather sophisticated algebra, some of which survive on clay tablets. Babylon’s mathematicians were already satisfied with good approximations from reference tables they compiled and not that concerned with exact numerical solutions to problems.
- They could answer quadratic equations using geometric drawings of areas and lengths of squares.
- From about 1550 BC, the Rhind Mathematical Papyrus contains Ancient Egyptian algebra, like: What must be the number (1 + ½ + ¼) to be multiplied by to give the answer 10?
- The Nine Chapters on the Mathematical Art from China were composed possibly between 1000 BC–200 AD and the eighth chapter, agricultural problems, gives rise to linear equations solved using rows of numbers similar to matrices.
- Modern historians of mathematics seldom wrangle over Book 2 of Euclid’s Elements from about 300 BC, debating whether it contains algebra written in the geometric language. Undeniably the great 11th-century Persian mathematician Omar Khayyam had no doubts.
- He argued for algebra to be seen as a legitimate branch of mathematics. Khayyam’s work with cubic equations gave him the reality that algebra and geometry are linked.
INTRODUCTION TO ARITHMETICA
- Diophantus tells us at the start of his classic work Arithmetica that he has written it as a textbook to help his friend Dionysius (and others probably) to answer mathematics problems.
- Arithmetica discusses the construction and solution of equations to find one or more unknowns.
- The whole copies of Arithmetica in Diophantus’ time were handwritten. Copies were produced by scribes for over a thousand years until the earliest copies were printed in Europe.
- Arithmetica may have been perceived in a similar way to Euclid’s Elements.
- Euclid compiled and, where necessary, improved on the work of mathematicians including Eudoxus and the Pythagoreans.
- Any different books dating from classical times with related themes to Arithmetica have been lost.
VOLUMES OF ARITHMETICA
- Diophantus wrote Arithmetica in thirteen volumes, of which six survived in Greek. Four exist as Arabic translations.
- The Arabic translations receive more commentary on the solutions than the Greek versions.
- It is probable that the Arabic editions were copied from the lost edition adjusted by Hypatia for the students at her school.
- Diophantus’ problems exercised the minds of several of the world’s best mathematicians for much of the next two millennia, with some particularly celebrated solutions provided by Brahmagupta, Pierre de Fermat, Joseph Louis Lagrange, and Leonhard Euler, among others.
THE MATHEMATICS IN ARITHMETICA
- Diophantus starts with definitions and rules.
- For example, he defines the results of the multiplication of quantities with various signs and tells his readers he will indicate subtraction with a symbol.
- He states: “A minus multiplied by a minus makes a plus; a minus multiplied by a plus makes a minus; and the sign of a minus is a truncated Ψ turned upside down, thus Diophantus-minus-sign.”
- Things get harder when Diophantus proceeds in this way, describing a different level of mathematical sophistication in Arithmetica.
- He introduces quadratics, cubics, and equations in higher powers of x.
- Diophantus neglects negative and irrational solutions to equations.
- In Arithmetica, Diophantus started the study of indeterminate equations. Indeterminate equations are polynomial equations in which the number of unknowns exceeds the number of equations given.
- The solutions to Diophantus’s indeterminate equations were always positive rational numbers.
- Diophantus was only interested in a single number of solutions, so he did not, for example, seek two numbers as solutions to quadratic equations.
- These days we define a Diophantine equation as an indeterminate equation whose solutions must be integers (whole numbers).
- The last Theorem of Fermat insists that if n is a whole number bigger than 2, the equation has no whole number solutions for x, y, and z.
This is a fantastic bundle which includes everything you need to know about the Diophantus across 22 in-depth pages. These are ready-to-use Diophantus worksheets that are perfect for teaching students about Diophantus who was an Alexandrian Hellenistic mathematician which is also known as the father of algebra. He was the author of a series of books called Arithmetica that solved hundreds of algebraic equations, approximately five centuries after Euclid’s era.
Complete List Of Included Worksheets
- Diophantus Facts
- Biographical Essay
- Selected Greek Mathematicians
- Father of Algebra
- Definition of Terms
- Book 1, Problem 1
- Diophantine Equations
- Importance of Arithmetica
- My Collection
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