Download presentation

Presentation is loading. Please wait.

Published byTyshawn Kehoe Modified over 2 years ago

1
2 feet How would you calculate the area of this circle ?...probably using the formula A = R 2 Since the diameter is 2 feet, Click your mouse for the next idea ! The constant , called “pi”, is about 3.14 so A = R 2 3.14 * 1 * 1 3.14 square feet means “about equal to” ? R 1 foot “R”, the radius, is 1 foot.

2
2 feet Click your mouse for the next idea ! ? LETS explore how people figured out circle areas before all this business ? The ancient Egyptians had a fascinating method that produces answers remarkably close to the formula using pi.

3
2 feet Click your mouse for the next idea ! ? The Egyptian Octagon Method Draw a square around the circle just touching it at four points. What is the AREA of this square ? 2 feet Well.... it measures 2 by 2, so the area = 4 square feet.

4
2 feet Click your mouse for the next idea ! The Egyptian Octagon Method 2 feet Now we divide the square into nine equal smaller squares. Sort of like a tic-tac-toe game ! Notice that each small square is 1/9 the area of the large one -- we’ll use that fact later !

5
2 feet Click your mouse for the next idea ! The Egyptian Octagon Method 2 feet Finally... we draw lines to divide the small squares in the corners in half, cutting them on their diagonals. Notice the 8-sided shape, an octagon, we have created ! Notice, also, that its area looks pretty close to that of our circle !

6
2 feet Click your mouse for the next idea ! The Egyptian Octagon Method 2 feet The EGYPTIANS were very handy at finding the area of this Octagon 1919 After all, THIS little square has an area 1/9 th of the big one... 1919 1919 1919 1919 And so do these four others... And each corner piece is 1/2 of 1/9 or 1/18 th of the big one 1. 18 1. 18 1. 18 1. 18

7
2 feet Click your mouse for the next idea ! The Egyptian Octagon Method 2 feet...and ALTOGETHER we’ve got... 1. 18 1. 18 1. 18 1. 18 4 pieces that are 1/18 th or 4/18 ths which is 2/9 ths 1919 1919 1919 1919 1919 Plus 5 more 1/9 ths For a total area that is 7/9 ths of our original big square

8
2 feet Click your mouse for the next idea ! The Egyptian Octagon Method 2 feet FINALLY...Yep, we’re almost done ! The original square had an area of 4 square feet. So the OCTAGON’s area must be 7/9 x 4 or 28/9 or 3 and 1/9 or about 3.11 square feet We have an OCTAGON with an area = 7/9 of the original square. 7979

9
AMAZINGLY CLOSE to the pi-based “modern” calculation for the circle ! 3.11 square feet3.14 square feet only about 0.03 off... about a 1% error !!

Similar presentations

OK

Why π ? Do you know why we must use 3.14 in all area and circumference formulas?

Why π ? Do you know why we must use 3.14 in all area and circumference formulas?

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on conservation and management of soil Ppt on kingdom monera organisms Ppt on world environment day Ppt on health care system Ppt on paintings and photographs related to colonial period literature Ppt on machine translation patent Ppt on nature and human ads Ppt on different mode of transportation Ppt on latest advancement in technology Ppt on principles of object-oriented programming concepts