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Activity1 Pi the mathematical constant (view source)
Revision as of 07:31, 15 July 2020
, 07:31, 15 July 2020no edit summary
=== Objectives ===
=== Objectives ===
Students will be able to understand the value of Pi is ratio of circle's circumference to its diameter.
===Estimated Time===
===Estimated Time===
20minutes
=== Prerequisites/Instructions, prior preparations, if any ===
=== Prerequisites/Instructions, prior preparations, if any ===
Know the concepts of circumference and diameter of a circle.
===Materials/ Resources needed===
===Materials/ Resources needed===
Digital resources:[https://karnatakaeducation.org.in/KOER/en/images/d/d8/Area_and_Perimeter_of_a_Polygon_inside_the_Circle.ggb Click here to open the geogebra file]
Non digital resources: Ruler
===Process (How to do the activity)===
===Process (How to do the activity)===
#[https://www.youtube.com/watch?v=_rJdkhlWZVQ&feature=youtu.be Click here for Finding Pi by Archimedes Method]. Archimedes approximated the value of Pi by starting with the fact that a regular hexagon inscribed in a unit circle has a perimeter of 6. He then found a method for finding the perimeter of a polygon with twice as many sides. Applying his method repeatedly, he found the perimeter of a 12, 24, 48, and 96 sided polygon. Using the perimeter as an approximation for the circumference of a circle he was able to derive an approximation for Pi equivalent to 3.14. This video uses a somewhat simpler method of doing the same thing and carries it out to polygons with millions of sides. All that is needed to understand the calculation is knowledge of the Pythagorean Theorem.
#[https://www.youtube.com/watch?v=_rJdkhlWZVQ&feature=youtu.be Click here for Finding Pi by Archimedes Method]. Archimedes approximated the value of Pi by starting with the fact that a regular hexagon inscribed in a unit circle has a perimeter of 6. He then found a method for finding the perimeter of a polygon with twice as many sides. Applying his method repeatedly, he found the perimeter of a 12, 24, 48, and 96 sided polygon. Using the perimeter as an approximation for the circumference of a circle he was able to derive an approximation for Pi equivalent to 3.14. This video uses a somewhat simpler method of doing the same thing and carries it out to polygons with millions of sides. All that is needed to understand the calculation is knowledge of the Pythagorean Theorem.
#Click here for Geogebra file{{Geogebra|zvbqkqa7}} which explains the value of Pi.
#[http://geogebratube.org/material/show/id/144079 Geogebra file] for explaining how 'circumference / diameter' is a constant, denoted as pi (Greek letter), using a number line
#[http://geogebratube.org/material/show/id/144079 Geogebra file] for explaining how 'circumference / diameter' is a constant, denoted as pi (Greek letter), using a number line
#An animation of the same concept.
#An animation of the same concept.
[[File:Pi 121.gif|400px|link=http://karnatakaeducation.org.in/KOER/en/index.php/File:Pi_121.gif]]
[[File:Pi 121.gif|400px|link=]]
*Process/ Developmental Questions
*Process/ Developmental Questions
Open the Geogebra file. Move the slider to 'unravel' the circumference' over the number line. Since the diameter is 1 unit (measuring from -0.5 to 0.5 on number line), the circumference ends at 3.14, showing the ratio between circumference
Open the Geogebra file. Move the slider to 'unravel' the circumference' over the number line. Since the diameter is 1 unit (measuring from -0.5 to 0.5 on number line), the circumference ends at 3.14, showing the ratio between circumference