Discovering Pi and its Measurement Variation: A Collaborative Cloud Activity

Scott Sinex and Ted Chambers

Department of Physical Sciences & Engineering

Prince George’s Community College

Conference on June 1-2, 2017 at The Community College of Baltimore County, Owings Mills

The measurement ...

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diameter

circumference

Measure to nearest 0.1 cm or 1 mm

Directions are on the “directions” tab on spreadsheet.

What do students discover?

  • Variation in the computation of pi and ways to assess variation
  • A mathematical model from plotting - circumference as a function of diameter
  • Computing the numerical value of pi from the data and slope of the model
  • Determining the percent error from known value of pi
  • Assessing the possible cause of error, both systematic & random
  • Consider a standard object to assess accuracy and precision

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Some definitions

Accuracy - closeness to true value, here the known value of pi

Precision - how reproducible is a measurement - range, standard deviation, %CV (coefficient of variation) = std. dev. * 100/mean

Percent Error = (experimental value - true value)*100/true value

Random Error = random scatter in data, can come from measurements, replicate measurements reduce

Systematic Error = bias in measurements

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Types of Errors

Data collection and sharing ...

Prebuilt spreadsheet in Google Sheets, part of the cloud-based Google Drive

To get the spreadsheet - https://goo.gl/oYVQzS

For today the file can be edited to collect data

Normally can view, then go to File > Make a copy… to get your copy which you can edit!

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Google Sheets is very Excel-like!

Examining variation - numerically & graphically

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Deriving a mathematical model C = 𝜋 d

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Best-fit line by linear regression

y = mx + b

y = mx

Computing 𝜋

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Percent Error = (experimental value - true value)*100

true value

Determining Accuracy & Precision

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Students get to ...

  • Engage in measurement & data collection/analysis
  • Compare individual, whole class, and other classes via in
  • Derive a mathematical model in terms of scientific variables:
          • y = mx C = 𝜋d
  • Examine goodness-of-fit with r-squared
  • Investigate error and how it influences the model parameters
  • Validate model via percent error using a standard via known value of pi

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We speculate ...

Value of pi will have a positive systematic error or positive %error.

Why? Measurement of diameter if not through center of object will be low; hence, pi will be larger than true/known value

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More on types of errors - S.A. Sinex (2005) Investigating Types of Errors, Spreadsheets in Education 2 (1) 115-124.

Rulers and Measurement Error (interactive Excel spreadsheet)

More information ...

Scott Sinex Email: sinexsa@pgcc.edu

Webpage: http://academic.pgcc.edu/~ssinex

Our thanks to Eric Curts for the original idea and spreadsheet!

http://www.controlaltachieve.com/2016/03/discovering-pi-with-google-sheets.html

Thanks for coming!!!

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MMATYC_2017 - Google Slides