Research and Lesson Plan: The History of Diophantine Equations a
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Mathematics
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University
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Hard
Standards-aligned
Larry Cooper
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12 Slides • 8 Questions
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Research and Lesson Plan: The History of Diophantine Equations and a Parametric Equations Lesson Plan
By Deanne Edman and Larry Cooper
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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
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Multiple Choice
Which equation is written in STANDARD form?
y = 1/2x + 2
y - 3 = -5(x + 2)
-7x + 2y = 9
3x + 2 = y
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Multiple Choice
The variable "t" is called a
parameter
parallel
paralegal
paradise
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Multiple Choice
Eliminate the parameter.
x = t and y = 5t
y=5x2
y=5x
y= x - 5
y=x2
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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)
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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
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Multiple Choice
The linear Diophantine equation 12x+16y = 18 is solvable.
True
False
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Research and Lesson Plan: The History of Diophantine Equations and a Parametric Equations Lesson Plan
By Deanne Edman and Larry Cooper
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