Three Classical Problems of Antiquity Using only a straightedge and a compass.

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Three Classical Problems of Antiquity Using only a straightedge and a compass

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Delian Problem: Delos

Transcript of Three Classical Problems of Antiquity Using only a straightedge and a compass.

Page 1: Three Classical Problems of Antiquity Using only a straightedge and a compass.

Three Classical Problems of Antiquity

Using only a straightedge and a compass

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Three Classical Problems of Antiquity(using only straightedge and compass)

• Delian Problem (Doubling the Cube)• Squaring the Circle• Trisecting a Given Angle

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Delian Problem: Delos

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Delos’ Highest Hill

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Terrace of the Lions

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Rene Descartes (1596-1650)

Constructible Numbers: a is constructible if and only if there exist two points on a number line a units apart: (a,0) or (0,a).

Lemma: If a and b are constructible numbers, then a+b, a-b, ab, a/b are also constructible.

Lemma: Square roots are constructible numbers.

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Pascal’s Triangle


Constructions Module 4 Lesson 1. Euclid created accurate geometric drawings using only a compass and a straightedge in ancient Greece. Architects still.

Constructions Module 4 Lesson 1. Euclid created accurate geometric drawings using only a compass and a straightedge in ancient Greece. Architects still.

Lesson and Comprehension Check 3mitchelldtech.weebly.com/uploads/3/7/5/6/37567383/3.6...straightedge and a compass to construct parallel and perpendicular lines. In Lesson 3-5, you

Lesson and Comprehension Check 3mitchelldtech.weebly.com/uploads/3/7/5/6/37567383/3.6...straightedge and a compass to construct parallel and perpendicular lines. In Lesson 3-5, you

Mrs. Rivas International Studies Charter School. Objective: To make basic construction using straightedge and compass. Vocabulary: Straightedge Straightedge.

Mrs. Rivas International Studies Charter School. Objective: To make basic construction using straightedge and compass. Vocabulary: Straightedge Straightedge.

Chapter 2 Construction Proving. Historical Background Euclid’s Elements Greek mathematicians used Straightedge Compass – draw circles, copy distances.

Chapter 2 Construction Proving. Historical Background Euclid’s Elements Greek mathematicians used Straightedge Compass – draw circles, copy distances.

Chapter 1.1 8/22/2015. Vocabulary point line collinear points plane compass straightedge sketch draw construct coplanar lines skew lines ray endpoint.

Chapter 1.1 8/22/2015. Vocabulary point line collinear points plane compass straightedge sketch draw construct coplanar lines skew lines ray endpoint.

Straightedge and Compass Constructions in the …orion.math.iastate.edu/dept/thesisarchive/TempFolder/... · Web viewAfter Euclid, geometry continued to evolve led by Archimedes,

Straightedge and Compass Constructions in the …orion.math.iastate.edu/dept/thesisarchive/TempFolder/... · Web viewAfter Euclid, geometry continued to evolve led by Archimedes,

ELLIPSES AND ELLIPTIC CURVES - Queen's U · 2014-11-18 · There is an ancient problem of constructing a square with straightedge and compass whose area equals . • Theorem: if you

ELLIPSES AND ELLIPTIC CURVES - Queen's U · 2014-11-18 · There is an ancient problem of constructing a square with straightedge and compass whose area equals . • Theorem: if you

Constructing a Nonagon Using Unmarked Straightedge and Compass Using the des Method

Constructing a Nonagon Using Unmarked Straightedge and Compass Using the des Method

Geometry Curriculum Framework - State Board of Education · g.co.12 4 Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective

Geometry Curriculum Framework - State Board of Education · g.co.12 4 Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective

with Teaching Notes - Appalachian State University · Web viewConstruct perpendicular lines, including the perpendicular bisector of a line segment. Using a compass and straightedge,

with Teaching Notes - Appalachian State University · Web viewConstruct perpendicular lines, including the perpendicular bisector of a line segment. Using a compass and straightedge,

Geometric Constructions Using a Compass and …… ·  · 2016-11-13Geometric Constructions Using a Compass and Straightedge ... 5. Perpendicular - lines that intersect to form right

Geometric Constructions Using a Compass and …… ·  · 2016-11-13Geometric Constructions Using a Compass and Straightedge ... 5. Perpendicular - lines that intersect to form right

Compass and Straightedge

Compass and Straightedge

Surprising Constructions with Straightedge and Compass · result is of no practical importance because an angle can be trisected using tools only slightly more advanced than a straightedge

Surprising Constructions with Straightedge and Compass · result is of no practical importance because an angle can be trisected using tools only slightly more advanced than a straightedge

Euclidean Geometry Rediscovered Geo Redisc. Mayer Kennesaw … · Naïve logic and set theory ... Definitions Constructions with straightedge and compass Eight axioms of plane geometry

Euclidean Geometry Rediscovered Geo Redisc. Mayer Kennesaw … · Naïve logic and set theory ... Definitions Constructions with straightedge and compass Eight axioms of plane geometry

Lesson 1: Construct an Equilateral Triangle · 2015. 7. 23. · GEOMETRY Lesson 2: Construct an Equilateral Triangle . Classwork . Opening Exercise . You will need a compass, a straightedge,

Lesson 1: Construct an Equilateral Triangle · 2015. 7. 23. · GEOMETRY Lesson 2: Construct an Equilateral Triangle . Classwork . Opening Exercise . You will need a compass, a straightedge,

Practice Tutorial PRACTICE & PROBLEM SOLVINGmathwithsiewert.pbworks.com/w/file/fetch/120316632/1.2 Practice Problems.pdfreport or poster. Part A Use a compass and straightedge to draw

Practice Tutorial PRACTICE & PROBLEM SOLVINGmathwithsiewert.pbworks.com/w/file/fetch/120316632/1.2 Practice Problems.pdfreport or poster. Part A Use a compass and straightedge to draw

Measuring and Constructing Angleslhsblogs.typepad.com/files/1.2-measure-and-construct-angles.pdf · For Exercises 1 and 2, use the figure shown. 1. Use a compass and straightedge

Measuring and Constructing Angleslhsblogs.typepad.com/files/1.2-measure-and-construct-angles.pdf · For Exercises 1 and 2, use the figure shown. 1. Use a compass and straightedge

Linear Geometric Constructions presentation.pdf · Compass Twice-Notched Straightedge Postulates for Neusis Constructions Using a straightedge and compass we can: Assume we can construct

Linear Geometric Constructions presentation.pdf · Compass Twice-Notched Straightedge Postulates for Neusis Constructions Using a straightedge and compass we can: Assume we can construct

Geometry Handbook - Tumwater Middle Web viewGeometry Handbook 2013-14. Name ... 3.1 ... G.2.C. Explain and perform basic compass and straightedge constructions related to parallel

Geometry Handbook - Tumwater Middle Web viewGeometry Handbook 2013-14. Name ... 3.1 ... G.2.C. Explain and perform basic compass and straightedge constructions related to parallel

Visit: Graphsheet : View the geometry output of entered commands in the command editor. The straightedge, setsquare, compass, protractor, and pencil graphics simulate the steps of

Visit: Graphsheet : View the geometry output of entered commands in the command editor. The straightedge, setsquare, compass, protractor, and pencil graphics simulate the steps of