Book contents
- Frontmatter
- Introduction
- Contents
- A Brief History of Mathematics Magazine
- Part I The First Fifteen Years
- Part II The 1940s
- Part III The 1950s
- Part IV The 1960s
- Part V The 1970s
- Part VI The 1980s
- Leonhard Euler, 1707–1783
- Love Affairs and Differential Equations
- The Evolution of Group Theory
- Design of an Oscillating Sprinkler
- The Centrality of Mathematics in the History of Western Thought
- Geometry Strikes Again
- Why Your Classes Are Larger than “Average”
- The New Polynomial Invariants of Knots and Links
- Briefly Noted
- The Problem Section
- Index
- About the Editors
Design of an Oscillating Sprinkler
from Part VI - The 1980s
- Frontmatter
- Introduction
- Contents
- A Brief History of Mathematics Magazine
- Part I The First Fifteen Years
- Part II The 1940s
- Part III The 1950s
- Part IV The 1960s
- Part V The 1970s
- Part VI The 1980s
- Leonhard Euler, 1707–1783
- Love Affairs and Differential Equations
- The Evolution of Group Theory
- Design of an Oscillating Sprinkler
- The Centrality of Mathematics in the History of Western Thought
- Geometry Strikes Again
- Why Your Classes Are Larger than “Average”
- The New Polynomial Invariants of Knots and Links
- Briefly Noted
- The Problem Section
- Index
- About the Editors
Summary
Editors' Note: Charles Bart Braden took his PhD at the University of Oregon, having written a dissertation on Lie algebras under the direction of Charles Curtis. He is now Professor Emeritus of Mathematics and Computer Science at Northern Kentucky University. Between 1994 and 1998 he was editor of the MAA's College Mathematics Journal. He is also the author of Discovering Calculus with Mathematica (Wiley, 1992).
For this paper he won the Allendoerfer Award in 1986 and two years later he won the Allendoerfer Award again for a paper entitled “Pólya's Geometric Picture of Complex Contour Integrals.”
The common oscillating lawn sprinkler has a hollow curved sprinkler arm, with a row of holes on top, which rocks slowly back and forth around a horizontal axis. Water issues from the holes in a family of streams, forming a curtain of water that sweeps back and forth to cover an approximately rectangular region of lawn. Can such a sprinkler be designed to spread water uniformly on a level lawn?
We break the analysis into three parts:
1. How should the sprinkler arm be curved so that streams issuing from evenly spaced holes along the curved arm will be evenly spaced when they strike the ground?
2. How should the rocking motion of the sprinkler arm be controlled so that each stream will deposit water uniformly along its path?
3. How can the power of the water passing through the sprinkler be used to drive the sprinkler arm in the desired motion?
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- Harmony of the World75 Years of Mathematics Magazine, pp. 229 - 236Publisher: Mathematical Association of AmericaPrint publication year: 2007