*Richard Evan Schwartz*

- Published in print:
- 2019
- Published Online:
- September 2019
- ISBN:
- 9780691181387
- eISBN:
- 9780691188997
- Item type:
- book

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691181387.001.0001
- Subject:
- Mathematics, Educational Mathematics

Outer billiards provides a toy model for planetary motion and exhibits intricate and mysterious behavior even for seemingly simple examples. It is a dynamical system in which a particle in the plane ...
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Outer billiards provides a toy model for planetary motion and exhibits intricate and mysterious behavior even for seemingly simple examples. It is a dynamical system in which a particle in the plane moves around the outside of a convex shape according to a scheme that is reminiscent of ordinary billiards. This book provides a combinatorial model for orbits of outer billiards on kites. The book relates these orbits to such topics as polytope exchange transformations, renormalization, continued fractions, corner percolation, and the Truchet tile system. The combinatorial model, called “the plaid model,” has a self-similar structure that blends geometry and elementary number theory. The results were discovered through computer experimentation and it seems that the conclusions would be extremely difficult to reach through traditional mathematics. The book includes an extensive computer program that allows readers to explore the materials interactively and each theorem is accompanied by a computer demonstration.Less

Outer billiards provides a toy model for planetary motion and exhibits intricate and mysterious behavior even for seemingly simple examples. It is a dynamical system in which a particle in the plane moves around the outside of a convex shape according to a scheme that is reminiscent of ordinary billiards. This book provides a combinatorial model for orbits of outer billiards on kites. The book relates these orbits to such topics as polytope exchange transformations, renormalization, continued fractions, corner percolation, and the Truchet tile system. The combinatorial model, called “the plaid model,” has a self-similar structure that blends geometry and elementary number theory. The results were discovered through computer experimentation and it seems that the conclusions would be extremely difficult to reach through traditional mathematics. The book includes an extensive computer program that allows readers to explore the materials interactively and each theorem is accompanied by a computer demonstration.

*Andrew Gelman and Deborah Nolan*

- Published in print:
- 2017
- Published Online:
- September 2017
- ISBN:
- 9780198785699
- eISBN:
- 9780191827518
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198785699.003.0003
- Subject:
- Mathematics, Educational Mathematics

Descriptive statistics is the typical starting point for a statistics course, and it can be tricky to teach because the material is more difficult than it first appears. The activities in this ...
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Descriptive statistics is the typical starting point for a statistics course, and it can be tricky to teach because the material is more difficult than it first appears. The activities in this chapter focus more on the topics of data displays and transformations, rather than the mean, median, and standard deviation, which are covered easily in a textbook and on homework assignments. Specific topics include: distributions and handedness scores; extrapolation of time series and world record times for the mile run; linear combinations and economic indexes; scatter plots and exam scores; and logarithmic transformations and metabolic rates.Less

Descriptive statistics is the typical starting point for a statistics course, and it can be tricky to teach because the material is more difficult than it first appears. The activities in this chapter focus more on the topics of data displays and transformations, rather than the mean, median, and standard deviation, which are covered easily in a textbook and on homework assignments. Specific topics include: distributions and handedness scores; extrapolation of time series and world record times for the mile run; linear combinations and economic indexes; scatter plots and exam scores; and logarithmic transformations and metabolic rates.

*Andrew Gelman and Deborah Nolan*

- Published in print:
- 2017
- Published Online:
- September 2017
- ISBN:
- 9780198785699
- eISBN:
- 9780191827518
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198785699.003.0005
- Subject:
- Mathematics, Educational Mathematics

This chapter addresses the descriptive treatment of linear regression with a single predictor: straight-line fitting, interpretation of the regression line and standard deviation, the confusing ...
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This chapter addresses the descriptive treatment of linear regression with a single predictor: straight-line fitting, interpretation of the regression line and standard deviation, the confusing phenomenon of “regression to the mean,” correlation, and conducting regressions on the computer. These concepts are illustrated with student discussions and activities. Many examples are of the sort commonly found in statistics textbooks, but the focus here is on how to work the examples into student-participation activities rather than simply examples to be read or shown on the blackboard. Topics include the following relationships: height and income, height and hand span, world population over time, and exam scores.Less

This chapter addresses the descriptive treatment of linear regression with a single predictor: straight-line fitting, interpretation of the regression line and standard deviation, the confusing phenomenon of “regression to the mean,” correlation, and conducting regressions on the computer. These concepts are illustrated with student discussions and activities. Many examples are of the sort commonly found in statistics textbooks, but the focus here is on how to work the examples into student-participation activities rather than simply examples to be read or shown on the blackboard. Topics include the following relationships: height and income, height and hand span, world population over time, and exam scores.