Research and Lesson Plan: The History of Diophantine Equations a

​ Research and Lesson Plan: The History of Diophantine Equations and a Parametric Equations Lesson Plan

 

By Deanne Edman and Larry Cooper

Diophantine Algebra

• He is often considered the "Father of Algebra".

• He wrote a series of books "Arithmetica".

• ​Of the thirteen books, only six have survived.

• ​Diophantine equations can be defined as polynomial equations.

• He was interested in integer solutions.​

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• Represents the end of a movement among Greeks away from geometrical algebra to a system of algebra that did not depend on geometry.

• Diophantus was a Greek Mathematician from Alexandria who was believed to have lived from (200-284) A.D.

Diophantine Algebra​ Continued

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Multiple Choice

What is the standard form of the equation of a line?

• y = mx + b

• Ax + By = C

• y - y₁ = m(x - x₁)

• y = Ax + By

Multiple Choice

Which equation is written in STANDARD form?

• y = 1/2x + 2

• y - 3 = -5(x + 2)

• -7x + 2y = 9

• 3x + 2 = y

Multiple Choice

The variable "t" is called a

• parameter

• parallel

• paralegal

• paradise

Multiple Choice

Eliminate the parameter.

x = t and y = 5t

• y=5x²

• y=5x

• y= x - 5

• y=x²

Multiple Choice

Find the point based on the parametric equations. t = 3

x = 1 - 2t

y =4t + 1

• (-5, 13)

• (13, -5)

• (5, 13)

• (13, 5)

Multiple Choice

The LDE ax+by = c is solvable if and only if

• d|a, where d=(a,b)

• d|b, where d=(a,b)

• d|c, where d=gcd(a,b)

• None of the above

Multiple Choice

The linear Diophantine equation 12x+16y = 18 is solvable.

• True

• False