Book contents
- Frontmatter
- Contents
- Introduction
- Newsletters and Commentaries
- 1 Arctangents
- 2 Benford's Law
- 3 Braids
- 4 CLIP Theory
- 5 Dots and Dashes
- 6 Factor Trees
- 7 Folding Fractions and Conics
- 8 Folding Patterns and Dragons
- 9 Folding and Pouring
- 10 Fractions
- 11 Integer Triangles
- 12 Lattice Polygons
- 13 Layered Tilings
- 14 The Middle of a Triangle
- 15 Partitions
- 16 Personalized Polynomials
- 17 Playing with Pi
- 18 Pythagoras's Theorem
- 19 On Reflection
- 20 Repunits and Primes
- 21 The Stern-Brocot Tree
- 22 Tessellations
- 23 Theon's Ladder and Squangular Numbers
- 24 Tilings and Theorems
- 25 The Tower of Hanoi
- 26 Weird Multiplication
- Appendices
- Index of Topics
- Classic Theorems Proved
- About the Author
17 - Playing with Pi
from Newsletters and Commentaries
- Frontmatter
- Contents
- Introduction
- Newsletters and Commentaries
- 1 Arctangents
- 2 Benford's Law
- 3 Braids
- 4 CLIP Theory
- 5 Dots and Dashes
- 6 Factor Trees
- 7 Folding Fractions and Conics
- 8 Folding Patterns and Dragons
- 9 Folding and Pouring
- 10 Fractions
- 11 Integer Triangles
- 12 Lattice Polygons
- 13 Layered Tilings
- 14 The Middle of a Triangle
- 15 Partitions
- 16 Personalized Polynomials
- 17 Playing with Pi
- 18 Pythagoras's Theorem
- 19 On Reflection
- 20 Repunits and Primes
- 21 The Stern-Brocot Tree
- 22 Tessellations
- 23 Theon's Ladder and Squangular Numbers
- 24 Tilings and Theorems
- 25 The Tower of Hanoi
- 26 Weird Multiplication
- Appendices
- Index of Topics
- Classic Theorems Proved
- About the Author
Summary
PUZZLER: A Rope Around the Earth
This puzzler is a classic:
A rope fits snugly around the equator of the Earth. Ten feet is added to its length. When the extended rope is wrapped about the equator, it magically hovers at uniform height above the ground. How high off the ground?
A second rope fits snugly about the equator of Mars and ten feet is added to its length. How high off the ground does this extended rope hover when wrapped about the planet's equator?
A third rope fits snugly about the (tiny) equator of a planet the size of a pea. When ten feet is added to its length, how high off the equator does it hover?
Comment. The answers to these questions are surprising in three ways: they are the same, they can be computed with no knowledge of the radius of the planet under consideration, and the shared answer is surprisingly large, about 1.6 feet. (Adding just ten feet to a rope the length of the circumference of the Earth produces enough space under which to roll!)
This problem provides a wonderful activity for students. Using a length of rope as a radius, draw a circle on the ground with sidewalk chalk. Lay a long rope about its circumference and add ten feet to its length. Have a group of students—evenly spaced about the circle—attempt to wrap this extended rope about the original circle with a gap of constant width.
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- Chapter
- Information
- Mathematics Galore!The First Five Years of the St. Mark's Institute of Mathematics, pp. 129 - 136Publisher: Mathematical Association of AmericaPrint publication year: 2012