Explanation The golden rectangle is the rectangle whose length of the sides is in the golden ratio that is approximately to 1 + 5 2 = 1.618033 . The golden rectangle can be constructed through pencil, ruler and compass. The steps are involved to construct the golden square. 1. Draw a square A B C D of side 1 cm. 2. Now consider a midpoint E on the side A B of the square and then draw a line from the midpoint to the corner of opposite side C . 3. Now extend the line from B 3. Now use the length E C as the radius and draw an arc from center E to the extended line. 4. Name the point F where the arc intersects the extended line. 5. Now draw a perpendicular line from point F and a perpendicular line from point C . 6. Name the point G where both the perpendicular lines intersect each other. 7. The resultant rectangle A F G D is a golden rectangle. The figure of the golden rectangle is shown in Figure 1. Figure 1 The base of the rectangle is A F and the height of the rectangle is A D . The length of A E and E B is 1 2 .and the length of B C is 1. The length of E C and E F are equal as both are radius. It can be seen that E B C is a right angle triangle. Use the Pythagoras theorem to obtain the length of the E F

The Heart of Mathematics: An Invitation to Effective Thinking, WileyPLUS NextGen Card with Loose-leaf Set Single Semester: An Invitation to Effective Thinking (Key Curriculum Press)

4th Edition

ISBN: 9781119760054

Author: Burger, Edward B. , Starbird, Michael

Publisher: Wiley (WileyPLUS Products)

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Chapter 4.3, Problem 24MS

To determine

To explain: The geometric construction of the golden rectangle.

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Chapter 4.3, Problem 23MS

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Chapter 4 Solutions

The Heart of Mathematics: An Invitation to Effective Thinking, WileyPLUS NextGen Card with Loose-leaf Set Single Semester: An Invitation to Effective Thinking (Key Curriculum Press)

Ch. 4.1 - The main event. State the Pythagorean Theorem.Ch. 4.1 - Two out of three. If a right triangle has legs of...Ch. 4.1 - Hypotenuse hype. If a right triangle has legs of...Ch. 4.1 - Assesing area. Suppose you know the base of a...Ch. 4.1 - Squares all around. How does the figure below...Ch. 4.1 - Operating on the triangle. Using a straightedge,...Ch. 4.1 - Excite your friends about right triangles....Ch. 4.1 - Easy as 1,2,3? Can there be a right triangle with...Ch. 4.1 - Sky high (S). On a sunny, warm day, a student...Ch. 4.1 - Sand masting (H). The sailboat named Sand Bug has...

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