Whiteboardmaths.com © 2004 All rights reserved 5 7 2 1.

Slides:



Advertisements
Similar presentations
P ARAMETRIC AND P OLAR I NTEGRATION. A REA E NCLOSED P ARAMETRICALLY Suppose that the parametric equations x = x(t) and y = y(t) with c  t  d, describe.
Advertisements

Draw and label on a circle:
Copyright © Cengage Learning. All rights reserved.
Loci The locus of a point is the path traced out by the point as moves through 2D or 3D space. In Loci problems you have to find the path for a given.
AREA AND CIRCUMFERENCE OF A CIRCLE. diameter radius circumference The perimeter of a circle is called the circumference (C). The diameter (d) of a circle.
10.2 Polar Equations and Graphs
M. Flórez, M.V. Carbonell, E. Martínez Dpto. Física y Mecánica. Escuela Técnica Superior de Ingenieros Agrónomos. Universidad Politécnica de Madrid (España)
Properties of Circles Perimeter and Area A circle is defined as a plane curve formed by the set of all points which are a given fixed distance from a.
9.2 Polar Equations and Graphs. Steps for Converting Equations from Rectangular to Polar form and vice versa Four critical equivalents to keep in mind.
Radius, Diameter, and Circumference of a Circle Lesson 7 (3 rd 6 Weeks) TEKS 6.6C.
1.You will explain the definition of a circle, radius, chord, diameter, circumference and arc. 2.You will name and label the terms of a circle. 3.You will.
1. 2 Circle A circle is the set of all points that are the same distance from a given point called the center.
3.4 Area and Circumference 1 Circle A circle is a plane figure that consists of all points that lie the same distance from a fixed point. The fixed point.
DEFINITIONS CYCLOID: INVOLUTE: SPIRAL: HELIX:
Cycloidal Excursions by Alexander Tir and John de St. Germain.
Undergraduate Seminar : Braselton/ Abell
The Cardioid. DESCRIPTION: The word ‘cardioid’ comes from the Greek root ‘cardi’ meaning heart. The Cardioid curve is a special case of the epicycloid.
10.8 Polar Equations and Graphs. An equation whose variables are polar coordinates is called a polar equation. The graph of a polar equation consists.
Circle Geometry.
10.1 Circles. Definition: Although all circles have the same shape, their sizes are determined by the measures of their radii. Two or more coplanar circles.
Circumference and Area: Circles
March 12, Trace the circle in your spiral. What is the distance around it?
Conics, Parametric Equations, and Polar Coordinates Copyright © Cengage Learning. All rights reserved.
AREA OF CIRCLES. REVIEW-CIRCUMFERENCE WORDS: The circumference of a circle is equal to pi times its diameter or pi times twice its radius. Symbols: or.
A circle is a closed curve in a plane. All of its points are an equal distance from its center.
Section 11.1 Curves Defined by Parametric Equations.
LESSON 7.6 AREA AND CIRCUMFERENCE OF CIRCLES OBJECTIVE: To use formulas for the circumference and area of circles.
Note 2: Perimeter The perimeter is the distance around the outside of a shape. Start at one corner and work around the shape calculating any missing sides.
1.8: Perimeter, Circumference, and Area
1 of 84 SHAPE AND SPACE Circles. 2 of 84 The circumference of a circle Use π = 3.14 to find the circumference of this circle. C = πd 8 cm = 3.14 × 8 =
Review Day! Hyperbolas, Parabolas, and Conics. What conic is represented by this definition: The set of all points in a plane such that the difference.
Whiteboardmaths.com © 2004 All rights reserved
Sullivan Algebra and Trigonometry: Section 9.2 Polar Equations and Graphs Objectives of this Section Graph and Identify Polar Equations by Converting to.
Whiteboardmaths.com © 2004 All rights reserved
Conics, Parametric Equations, and Polar Coordinates 10 Copyright © Cengage Learning. All rights reserved.
Question 1 Write the equation of the circle: Center: (-7, 14) Area: 81π.
Circumference Review. Review What is the relationship between a radius and a diameter? What does a circumference measure? What formulas do we use to calculate.
Shape and Space CIRCLE GEOMETRY. Circle Geometry Rule 1 : ANGLE IN A SEMICIRCLE = 90° A triangle drawn from the two ends of a diameter will always make.
SUBMITTED BY ROSHNI B S. Circle is a closed curve in a plane A circle can be drawn with the help of a circular object.
Review:labeled part Write the name of each of the circle E. B. C. A. D.
Conics Conics Review. Graph It! Write the Equation?
Chapter 26 Circles & Other Shapes. Circumference Remember circumference = distance around the outside of a circle C = π × d OR C = 2 × π × r.
Circles…… Area and Circumference The Circumference of a Circle Find the circumference of the following circles. C =  d C = 2  r 8 cm cm 2 C =
Double Integrals in Polar Coordinates
Chapter 17 Section 17.4 The Double Integral as the Limit of a Riemann Sum; Polar Coordinates.
© T Madas. What is an epicycloid? Imagine a circle rolling on the outside of another circle. Pick a fixed point on the rolling circle and follow its path.
CurveCurve StitchingStitching 2 Parabolas 4 Parabolas.
Circle Radius Diameter Tangent Circumference. Angles subtended by the same chord are equal Chord.
Closed curves Simple Closed Curves Simple closed curves made of line segments.
Copyright © Cengage Learning. All rights reserved. 12 Geometry.
Introduction & Installation. Circles A circle is a shape with all points the same distance from the center. A circle is named by the center. The circle.
8. Polar Coordinates I am the polar curve r = sin(2^t)-1.7.
Definition: A plane curve is a set C of ordered pairs (f(t), g(t)), where f and g are continuous functions on an interval I. The graph of C consists of.
Worksheets Demo 1 Demo 2 Demo 3 Demo 4.
Equations Parametric.
Unit 5: Perimeter, Circumference & Area of Polygons & Circles
Curve Stitching.
8.2 Polar Equations and Graphs
Drawing a cardioid Font: Arial Rounded MT Bold
THE WORLD OF SHAPES CIRCLES.
The Cardioid.
Graphing Polar Equations
SHAPES By: Ms. Conquest.
15.4 Double Integrals in Polar Form
Section 6.4 Graphs of Polar Equations
Intro to Algebra/Geometry
Introduction to Circles
Circle Theorems Give a REASON for each answer
10.1 Circles.
Plane Curves and Parametric Equations
Presentation transcript:

Whiteboardmaths.com © 2004 All rights reserved 5 7 2 1

A n i m a t e d C u r v e S t i t c h i n g

Black 5 Curve Stitching

Demo 1 2 Parabolas

Demo 2 8 Parabolas

Demo 3 4 Parabolas

Demo 4 8 Parabolas

Rose Demo How many lines? Sum (1 to 17) (17 x 18)/2 = 153

The Epicycloids is the name given to the family of curves that are traced out by the path of a point on the circumference of a circle, that rolls around the outside of a fixed circle of different radii. Epicycloids r 2r r r Cardioid(Single Cusp) (Heart Shaped) Nephroid (Double Cusp) (Kidney Shaped) 3r Epicycloid of Cremona named after the mathematician

Cardiod Cardioid Moving Cardioid A Cardiod is the name given to the curve that is traced out by the path of a point on the circumference of a circle that rolls around the outside of a fixed circle of equal radius. Cardiod Cardioid Moving Cardioid r r Fixed Circle

Nephroid Moving Nephroid Nephroid A Nephroid is the name given to the curve that is traced out by the path of a point on the circumference of a circle that rolls around the outside of a fixed circle of twice its radius. Nephroid Moving Nephroid r 2r Fixed Circle Nephroid

Epicycloid Moving Epycycloid Epicycloid of Cremona The Epicycloid of Cremona is the name given to the curve that is traced out by the path of a point on the circumference of a circle that rolls around the outside of a fixed circle of 3 times its radius. Epicycloid Moving Epycycloid r 3r Fixed Circle Epicycloid of Cremona

Cardioid n  2n Cardioid Auto Single Cusp

Cardioid Demo n  2n Cardioid Single Cusp 72 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 144 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 Cardioid n  2n Cardioid Demo Single Cusp

Nephroid n  3n Nephroid Auto Double Cusp

Nephroid Demo n  3n Nephroid Double Cusp 72 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 144 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 Nephroid n  3n Nephroid Demo Double Cusp

Epicycloid of Cremona n  4n Epicycloid Auto Triple Cusp

Epicycloid Demo n  4n Epicycloid of Cremona Triple Cusp 72 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 144 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 Epicycloid of Cremona n  4n Epicycloid Demo Triple Cusp

Black 1 2 Parabolas

Black 2 8 Parabolas

Black3 4 Parabolas

Black4 8 Parabolas

Black 5 18 Point Mystic Rose

Static1

Static 2

Static3

Static 4

Static 5

Static 6

Cardioid n  2n Static 7

Nephroid n  3n Static 8

Epicycloid of Cremona n  4n Static 9

Worksheets

72 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 144 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143

Feedback: Privacy Policy Feedback
Do Not Sell My Personal Information
About project: SlidePlayer Terms of Service

© 2025 SlidePlayer.com. Inc. All rights reserved.