“The greatness of a population is measured by the ideas it owns."

Slides:

Advertisements

Similar presentations

PI And things it concerns. What is pi? Here are two different dictionary definition of pi : the ratio of the circumference to the diameter of a circle;

Advertisements

History of Pi By Julian Wolf. Babylonian Pi  The ratio of the circumference to the diameter of a circle is constant (namely, pi) has been recognized.

History of Pi By, Travis Nitko. The Beginning The first time Pi was used in an equation was when Archimedes used it to find the area of a circle with.

The History of Pi By John Wallace. What is Pi? Pi is the ratio of the circumference of a circle to its diameter. Pi is approximately

The Origin and History of Pi CTAE Resource Network Instructional Resources Office Written by: Philip Ledford and Dr. Frank Flanders July 2009.

Lesson Objectives 1.You will gain a deeper understanding of the fundamental concept of area of a circle. 2.You will understand how the formula for the.

Geometric Shapes and Area

Introduction You have used the formulas for finding the circumference and area of a circle. In this lesson, you will prove why the formulas for circumference.

S5 Int 1 The Circle Circumference of the circle Main Parts of a Circle Investigation of the Ratio of Circle Composite shapes Perimeter.

National 4 EF 1.2a The Circle Circumference of the circle Diameter = Circumference ÷ π Area of a circle Composite Area Main Parts.

1 The number  is defined as the ratio of the circumference of a circle to its diameter. What is  ? CS110: Introduction to Computer Science: Lab Module.

Archimedes The Archimedes Portrait XVII century Domenico Fetti.

Discovery of Pi Ksenia Bykova.

Pi Day Celebration. Happy Pi Day "Probably no symbol in mathematics has evoked as much mystery, romanticism, misconception and human interest as the number.

Pythagorean Triples Big Idea:.

6 th Grade Supporting Idea: Geometry and Measurement Teacher Quality Grant.

Circumference of a Circle Parts of a circle Calculate d from r Calculate r from d Introducing pi Using C =π d C from d …. 5 circles C given radius 5 questions.

Introducing Pi Pi Day 3.14 March 14, 2015 What is Pi? Pi is the ratio of the circumference of a circle to the diameter. = Circumference of circle / Diameter.

Lesson Objectives 1.You will gain a deeper understanding of the fundamental concept of pi. 2.You will discover that there is a special relationship between.

PI: Food Group or Math Concept? Pi Day Presentation.

Level 2 Wednesday, 19 August 2015Wednesday, 19 August 2015Wednesday, 19 August 2015Wednesday, 19 August 2015Created by Mr Lafferty1.

13.2 General Angles and Radian Measure. History Lesson of the Day Hippocrates of Chois ( BC) and Erathosthenes of Cyrene ( BC) began using.

Formulae Perimeter Formulae for Polygons.

Chapter 10.4 Notes: Use Inscribed Angles and Polygons

Inscribed Angles By the end of today, you will know what an inscribed angle is and how to find its measure.

Introduction to Limits. What is a limit? A Geometric Example Look at a polygon inscribed in a circle As the number of sides of the polygon increases,

Spring 2007Mrs. Bubello Circumference. Spring 2007Mrs. Bubello Circumference Objectives To identify the parts of a circle. To derive a formula for circumference.

Introduction to Limits Section 1.2. What is a limit?

Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. 5.3 Multiplying Decimals and Circumference of a Circle.

Circles: Circumference & Area Tutorial 8c A farmer might need to find the area of his circular field to calculate irrigation costs.

© T Madas Μη μο υ το υ ς κύκλους τάρα τ τε. The approach of Archimedes for approximating π.

Archimedes The area of the unit circle.  Archimedes ( B.C.) sought a way to compute the area of the unit circle. He got the answer correct to.

Measuring the Circle: The Story of Eric Wishnie Seth Coldsmith.

6 th Grade Supporting Idea: Geometry and Measurement Teacher Quality Grant.

Section 4-2 Area and Integration. Basic Geometric Figures rectangle triangle parallelogram.

Ancient Mathematicians for A Day: The calculation of pi Georgia CTAE Resource Network Instructional Resources Office Written By: Philip Ledford and Dr.

A PI-Day Activity Let’s do . Cutting π Materials Circular object (ball); string; scissors; tape To Do and Notice Carefully wrap string around the circumference.

Area Under the Curve We want to approximate the area between a curve (y=x 2 +1) and the x-axis from x=0 to x=7 We want to approximate the area between.

Circumference of a Circles

Circles, Polygons and Area WHAT CAN YOU DEDUCE, GIVEN VERY LITTLE INFORMATION?

BY: LEONARDO BENEDITT Mathematics. What is Math? Mathematics is the science and study of quantity, structure, space, and change. Mathematicians.

Circles, Polygons, Circumference and Perimeter WHAT CAN YOU DEDUCE, GIVEN VERY LITTLE INFORMATION?

 Bell Work Directions: Take the NOTES on the back table. Answer the following questions on your NOTES! 1) How was ‘math’ created? 2) How was ‘science’

Diameter Radius.

Section 11-4 Areas of Regular Polygons. Given any regular polygon, you can circumscribe a circle about it.

SHERRI BROGDON THE IRRATIONAL WORLD OF PI. DEFINITION AND VOCABULARY OF PI Definition of pi is the ratio of the circumference to the diameter of a circle.

Limits. We realize now, that making “h” smaller and smaller, will allow the secant line to get closer to the tangent line To formalize this process, we.

Inscribed and Circumscribed Polygons Inscribed n If all of the vertices of a polygon lie on the circle, then the polygon is inscribed.

Inscribed Angles By the end of today, you will know what an inscribed angle is and how to find its measure.

Estimating the Area of a Circle Math 8 Stewart COPY SLIDES THAT HAVE A PENCIL.

Archimedes Limits by Archimedes of Syracuse. There is a fascinating history about how they made an attempt to calculate the area of a circle.

Lesson 4: Proving Area of a Disk STUDENTS USE INSCRIBED AND CIRCUMSCRIBED POLYGONS FOR A CIRCLE (OR DISK) OF RADIUS AND CIRCUMFERENCE TO SHOW THAT THE.

Great mathematics Prepared by Dmitry Podgainyi M-12.

Pi By Tracy Hanzal.

VOLUME OF SOLIDS.

4 Chapter Chapter 2 Decimals.

March 14th is Pi Day Complete 6-10 on the WAM Sheet HW Questions?

Π Happy Pi Day!.

Chapter #1 Presentation

Forging new generations of engineers

Geometric Shapes and Area

Geometric Shapes and Area

10.7 Inscribed and Circumscribed Polygons

Japanese Wazan Mathematician

Circumference of Circles

The Origin and History of Pi

Forging new generations of engineers

Forging new generations of engineers

? How would you calculate the area of this circle ?

Circumference of Circles

Presentation transcript:

“The greatness of a population is measured by the ideas it owns."

The big difference between Hellenistic science and previous science is the introduction of the scientific method. It has allowed the achievement of a technological level equal to that of 17 th -century Europe.

Integrals Archimedes of Syracuse (Syracuse, 287 b.C. – Syracuse, 212 b.C.), a mathematician, an engineer, a physicist and an ancient Greek inventor (Siceliot), was one of the greatest scientists of history.

Greek «Pi» is a mathematical constant which is indicated with, which is used a lot in science. Since antiquity a lot of civilizations have tried to define its value. Babylonians = 3… But it’s by defect! Egyptians 2 =3,160… But it’s by excess!

Archimedes understood that the measurement of the circle was comprehended between the perimeters of an inscribed and a circumscribed polygon. The more sides the polygons have, the closer one gets to the exact value of. Let’s imagine a circle whose diameter equals 1 and two squares, one inscribed and another circumscribed. The perimeter of the inscribed square is 4. = 2,828. The perimeter of the circumscribed square is 4 · 1= 4, therefore 2,828 < < 4 S = 1 C= If we consider an inscribed and a circumscribed hexagon… … 3,0< < 3,21539

Then Archimedes progressively doubled the sides of the two polygons up to two 96-side polygon. He noticed that the more sides the polygons had, the more defined the value of … Today we know that… … 3,140 < < 3,142

Number of sides Side measure of the inscribed polygon Side measure of the circumscribed polygon Perimeter of the inscribed polygon Perimeter of the circumscribed polygon VALUE OF 61, , , , , <π<3, , , , , , <π<3, , , , , , <π<3, , , , , , <π<3, , , , , , <π<3, , , , , , <π<3, , , , , , <π<3, , , , , , <π<3, , , , , , <π<3, , , , , , <π<3, , , , , , <π<3, , , , , , <π<3, , , , , , <π<3, , , , , , <π<3, , , , , , <π<3, , , , , <π<3, HOW TO CALCULATE THE VALUE OF THROUGH THE PERIMETER OF THE INSCRIBED AND CIRCUMSCRIBED POLYGONS

Number of sides Value of DIFFERENT INTERVALS OF

Value of Number of sides Area of the inscribed polygon Area of the circumscribed polygon GRAPHIC OF THE APPROXIMATION OF