Presentation is loading. Please wait.

Presentation is loading. Please wait.

Golden Rectangle  A golden rectangle is a rectangle whose side lengths are in the golden ratio, 1:φ.  The golden ratio, φ, is pronounced “Fee” and is.

Published by Modified over 9 years ago

Similar presentations

Presentation on theme: "Golden Rectangle  A golden rectangle is a rectangle whose side lengths are in the golden ratio, 1:φ.  The golden ratio, φ, is pronounced “Fee” and is."— Presentation transcript:

1 Golden Rectangle  A golden rectangle is a rectangle whose side lengths are in the golden ratio, 1:φ.  The golden ratio, φ, is pronounced “Fee” and is approximately 1.618. 1 φ

2 Constructing a Golden Rectangle 1.) Construct a unit square 2.) Draw a line from the midpoint of one side to an opposite corner. 3.) Use that line as the radius to draw an arc that defines the long dimension of the rectangle. Midpoint Square

3 Constructing a Golden Rectangle The Golden Rectangle φ 1

4 Proving a Golden Rectangle Pythagorean Theorem  We will have to use the Pythagorean Theorem Ratio = Longer Side Shorter Side = = 1.618 Golden RatioPhi Which is the “Golden Ratio” or “Phi”

5 “Golden Rectangle”, GSP, and Pictures 1.) Construction of the Golden Rectangle using GSP. 2.) Parthenon (using pictures). 3.) Mona Lisa (using pictures).

6 Quadrature of the Rectangle

Download ppt "Golden Rectangle  A golden rectangle is a rectangle whose side lengths are in the golden ratio, 1:φ.  The golden ratio, φ, is pronounced “Fee” and is."

Similar presentations

Problem Solving with Quadratics. Problem Solving Guide:

Problem Solving with Quadratics. Problem Solving Guide:
      H-13 

      H-13 
The Distance Formula Lesson 9.5.

The Distance Formula Lesson 9.5.
Whiteboardmaths.com © 2004 All rights reserved 5 7 2 1.

Whiteboardmaths.com © 2004 All rights reserved
A Ratio That Glitters Exploring Golden Ratios. Golden Ratio in Architecture The Pyramid of Khufu has the Golden Ratio in the ratio of the height of the.

A Ratio That Glitters Exploring Golden Ratios. Golden Ratio in Architecture The Pyramid of Khufu has the Golden Ratio in the ratio of the height of the.
Special Right Triangles

Special Right Triangles
The Pythagorean Theorem x z y. For this proof we must draw ANY right Triangle: Label the Legs “a” and “b” and the hypotenuse “c” a b c.

The Pythagorean Theorem x z y. For this proof we must draw ANY right Triangle: Label the Legs “a” and “b” and the hypotenuse “c” a b c.
 Pythagoras was especially interested in the golden section, and proved that it was the basis for the proportions of the human figure. He showed that.

 Pythagoras was especially interested in the golden section, and proved that it was the basis for the proportions of the human figure. He showed that.
The Golden Ratio Math in Beauty, Art, and Architecture.

The Golden Ratio Math in Beauty, Art, and Architecture.
Direct Analytic Proofs. If you are asked to prove Suggestions of how to do this Two lines parallel Use the slope formula twice. Determine that the slopes.

Direct Analytic Proofs. If you are asked to prove Suggestions of how to do this Two lines parallel Use the slope formula twice. Determine that the slopes.
Geometry Section 9.4 Special Right Triangle Formulas

Geometry Section 9.4 Special Right Triangle Formulas
ISOMETRIC CIRCLE.

ISOMETRIC CIRCLE.
Geometry Tactile Graphics Kit. Drawings 1 - 2 #1. Perpendicular to a line#2. Skew lines and transversal.

Geometry Tactile Graphics Kit. Drawings #1. Perpendicular to a line#2. Skew lines and transversal.
Quadrilaterals in the Coordinate Plane I can find the slope and distance between two points I can use the properties of quadrilaterals to prove that a.

Quadrilaterals in the Coordinate Plane I can find the slope and distance between two points I can use the properties of quadrilaterals to prove that a.
The Mathematical Formula of Art

The Mathematical Formula of Art
Pythagorean Theorem and Its Converse Objective To use the Pythagorean Theorem and its converse Essential Understanding: If you know the lengths of any.

Pythagorean Theorem and Its Converse Objective To use the Pythagorean Theorem and its converse Essential Understanding: If you know the lengths of any.
The Pythagorean Theorem

The Pythagorean Theorem
Right Triangles And the Pythagorean Theorem. Legs of a Right Triangle Leg -the two sides of a right triangle that form the right angle Leg.

Right Triangles And the Pythagorean Theorem. Legs of a Right Triangle Leg -the two sides of a right triangle that form the right angle Leg.
Right Triangles and Trigonometry Chapter 8. Pythagorean Theorem a 2 + b 2 = c 2 right triangle a 2 + b 2 < c 2 obtuse triangle a 2 + b 2 > c 2 acute triangle.

Right Triangles and Trigonometry Chapter 8. Pythagorean Theorem a 2 + b 2 = c 2 right triangle a 2 + b 2 < c 2 obtuse triangle a 2 + b 2 > c 2 acute triangle.
The Golden Ratio Lynn DeRosa Carole McMahon Carol Herb.

The Golden Ratio Lynn DeRosa Carole McMahon Carol Herb.

Similar presentations

Ads by Google