17 Sides By Mike Frost. What Can You Construct with Straight Edge and Compass? Lengths can be multiplied.

Slides:

Advertisements

Similar presentations

Objective: To describe properties of solid shapes such as perpendicular and parallel lines, faces and edges.

Advertisements

Polygon from a known side

MAT 320 Spring  You may remember from geometry that you can perform many constructions only using a straightedge and a compass  These include.

12.5 Surface Area of Pyramids By Tosha Williams, Taylor Clear, and Jessica Strassle.

Trial and Improvement Practice © T Madas.

7.3 Formulas involving polygons

Interior angles of polygons This is just one of the six interior angles of this polygon.

Geometry The Shapes Around Us.

2 D shapes only have two dimensions, such as width and length Some are: Polygons and Some are: Not Polygons.

1.Start with the number of sides in a pentagon. 2.Add the number of sides in a triangle. 3.Divide by the number of sides in an octagon. 4.Multiply by.

EXAMPLE 1 Find the area of a lateral face of a pyramid SOLUTION Use the Pythagorean Theorem to find the slant height l. l 2 = Write formula. l.

Objective: To describe properties of solid shapes such as perpendicular and parallel lines, faces and edges.

Constructible Numbers By Brian Stonelake. The Three Problems of Antiquity Roughly 2500 years ago, the Ancient Greeks wondered if it is possible to: –

Explore Solids Warm Up Lesson Presentation Lesson Quiz.

1 Mersenne Primes How to generate more prime numbers? Mersenne ( ) generated primes using formula: where p is a prime M 2 = 3; M 3 = 7, M 5 = 31,

Polygons By Ryan.

Perimeter & Area Lessons 19 & 20.

Chapter 6 Polygons. Definitions Polygon – many sided figure 3 sided – triangles 4 sided – quadrilaterals 5 sided – pentagons 6 sided – hexagons 7 sided.

Who Wants To Be A Millionaire?

Find the area of each square. How do you find the area of each square? Area may be found by either counting the number of units or multiply length of.

Constructions. Supplies Paper (thick stack) Compass Straight Edge.

9-2 Area of Regular Polygons The center of a regular polygon is equidistant from its vertices. Radius- the distance from the center to a vertex. Apothem-

Lesson 12.1 Exploring Solids Today, we will learn to… > use vocabulary associated with solids > use Euler’s Formula.

Geometry in a House By: Barbara Soares. Points, Lines and Ray Parallel Lines Parallel lines are lines that never intersect. On this picture the sides.

Holt CA Course Perimeter Warm Up 1. What figure has four equal sides and four right angles? 2. What figure has eight sides? 3. What figure has five.

Warm-Up 1)Solve for x 2)Solve for x 142° (x-11)° 81° (9x)°

7.3 Formulas Involving Polygons. Before We Begin.

9-7 Perimeter Course 1 Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day.

Section 11-2 Areas of Regular Polygons. Area of an Equilateral Triangle The area of an equilateral triangle is one fourth the square of the length of.

parallel lines never touch Make 90° angles (paper can fit in the corner)

Powers and roots. Square each number a) 7 b) 12 c) 20 d) 9 e) 40 a) 49 b) 144 c) 400 d) 81 e) 1600.

Polygons Shapes with many sides! Two-dimensional Shapes (2D) These shapes are flat and can only be drawn on paper. They have two dimensions – length.

Chapter 1: Square Roots and the Pythagorean Theorem Unit Review.

Perimeter LESSON 19 POWER UP CPAGE 128. Perimeter The distance around the outside Find any missing sides Add all the sides together 6 cm 5 cm.

Year 8: Constructions Dr J Frost Last modified: 27 th September 2015.

M4G1 Students will define and identify the characteristics of geometric figures through examination and construction. M4G2 Students will understand fundamental.

~Adapted from Walch Education Applying Lines of Symmetry.

The #’s 1, 4, 9, 16, 25.…are called. The #’s 1, 4, 9, 16, 25.…are called perfect squares / square numbers.

Holt CA Course Perimeter Warm Up Warm Up Lesson Presentation Lesson Presentation California Standards California StandardsPreview.

Perimeter! What’d you say? Yeeeah….perimeter. The distance around straight edged THINGS! We call ‘em POLYGONS!

Area of a Parallelogram. What is a parallelogram? A parallelogram is a 4-sided shape formed by two pairs of parallel lines. Opposite sides are equal in.

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

160 as a product of its prime factors is 2 5 x 5 Use this information to show that 160 has 12 factors.

Constructing Triangles Tri 1 side/2 angles Constructions Example 1: To construct a triangle of base 9 cm with angles of 35 o and 65 o. To construct a.

Lesson 7.2: Cube roots Objectives: To determine the cube root of a number. To Solve a cube root equation. EQ: How do you evaluate a cube root expression?

9-7 Perimeter Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day Lesson Quizzes Lesson Quizzes.

Area of Regular Polygons Terms Radius – segment joining the center of the polygon to the vertex of the polygon. All radii of a polygon are equal. When.

Plane Figures. What are the types of figures? A closed figure begins and ends at the same end point. An open figure has ends that do not meet.

House Fire House. Can you find one or more acute angles? An acute angle is an angle with a measure of less than 90 degrees.

Remember: A cube is a three dimensional (3-D) prism with 6 square faces; so all sides are congruent(same) and all angles are right angles. Perfect Cubes.

Constructions. History Geometric constructions: what can be built with just a straight-edge and a compass Ancient Greeks asked many questions about constructions:

7.3 Formulas involving polygons

6.1 The Polygon Angle-Sum Theorem

Problem of the Day Solve for y, justify your answer 15x (x + 7)

Name the polygon by the number of sides.

Lesson 8-1 Angles of Polygons Lesson 3-4: Polygons.

Regular Geometry Shapes

Polygons – Measurements of Angles

We remember the sum of the interior angles in a triangle is 180 degrees.

Ms. Brittany Uribe Geometry

5 Construction 4 Line Perpendicular to a Given Line l, Passing Through a Given Point on l Method 1: solution Using a Set Square Line up one side of er.

5 Construction 2 Perpendicular Bisector of a Segment, Using Only Compass and Straight Edge Draw a line segment [CD]. Place the compass needle point on.

An angle inside a polygon

11.5 Areas of Regular Polygons

Finding the Area of Rectangles and Parallelograms

Square and Cube Roots.

9-7 Perimeter Course 1 Warm Up Problem of the Day Lesson Presentation.

PYTHAGORAS EXPLAINS THEIR RELATIONSHIP!!

Regular Polygons:.

Presentation transcript:

17 Sides By Mike Frost

What Can You Construct with Straight Edge and Compass? Lengths can be multiplied

Lengths can be halved by Dropping a Perpendicular

Angles can be Halved

Square Roots can be taken But you can’t: Trisect an Angle or take Cube Roots

Constructing the Pentagon

Carl Friedrich Gauss To construct a Polygon with a prime number of sides n, n must be a Fermat Prime, of the form: F 0 = 3 F 1 = 5 F 2 = 17 F 3 = 257 F 4 = 65, 537 Five known Fermat Primes N=0,1,2,3,4

“Dr Euler’s Fabulous Formula” – by Paul Nahin

Cos (2 π / 17)... Cos (2 π / 3) = -0.5 Cos (2 π / 5) = (-1 + sqrt(5) ) / 4 Cos (2 π / 257) ?

...and Cos (2π/65,537) ??

The Biggest Constructible Odd-Numbered Polygon = 4, 294, 967, 295 Sides

Constructing the 17-Gon