Mar1998thinkitover_integral Distances A Problem From Paul Erdös
This document was uploaded by user and they confirmed that they have the permission to share it. If you are author or own the copyright of this book, please report to us by using this DMCA report form. Report DMCA
Overview
Download & View Mar1998thinkitover_integral Distances A Problem From Paul Erdös as PDF for free.
More details
- Words: 327
- Pages: 1
THINK IT OVER
Think It Over
This section of Resonance is meant to raise thought-provoking, interesting, or just plain brain-teasing questions every month, and discuss answers a few months later. Readers are welcome to send in suggestions for such questions, solutions to questions already posed, comments on the solutions discussed in the journal, etc. to Resonance, Indian Academy of Sciences, Bangalore 560 080, with “Think It Over” written on the cover or card to help us sort the correspondence. Due to limitations of space, it may not be possible to use all the material received. However, the coordinators of this section (currently R Nityananda and C S Yogananda) will try and select items which best illustrate various ideas and concepts, for inclusion in this section. Shailesh Shirali Principal, Rishi Valley School Chittoor District Rishi Valley 517 352, India
Integral Distances : A Problem from Paul Erdös
As a sampler of Erdös’ early work in combinatorial geometry, we offer a problem proposed by Paul Erdös and N H Anning in 1945 in a paper titled ‘Integral Distances’. The problem is the following. Show that (a) for any integer n > 2 one can find n distinct points in a plane, not all on a line, such that the distances between them are all integers; (b) it is impossible to find infinitely many points, not all on a line, with this property.
J V Narlikar Director, Inter-University Centre for Astronomy & Astrophysics Ganeshkhind, Post Bag 4 Pune 411 007, India Ph - 91-212-351414 and 359415 Fax - 91-212-356417 E-mail: [email protected]
A Burning Question
You are given two non-identical, nonuniform laces. Each takes one hour to burn. Being non-uniform, equal lengths don’t burn in equal times. How will you burn them to determine a time interval of 45 minutes ? A more difficult variation on this: You now have only one such lace. How will you burn it to determine only 15 minutes ? __________________________________________________________________________
70
RESONANCE ⎜ March 1998
Think It Over
This section of Resonance is meant to raise thought-provoking, interesting, or just plain brain-teasing questions every month, and discuss answers a few months later. Readers are welcome to send in suggestions for such questions, solutions to questions already posed, comments on the solutions discussed in the journal, etc. to Resonance, Indian Academy of Sciences, Bangalore 560 080, with “Think It Over” written on the cover or card to help us sort the correspondence. Due to limitations of space, it may not be possible to use all the material received. However, the coordinators of this section (currently R Nityananda and C S Yogananda) will try and select items which best illustrate various ideas and concepts, for inclusion in this section. Shailesh Shirali Principal, Rishi Valley School Chittoor District Rishi Valley 517 352, India
Integral Distances : A Problem from Paul Erdös
As a sampler of Erdös’ early work in combinatorial geometry, we offer a problem proposed by Paul Erdös and N H Anning in 1945 in a paper titled ‘Integral Distances’. The problem is the following. Show that (a) for any integer n > 2 one can find n distinct points in a plane, not all on a line, such that the distances between them are all integers; (b) it is impossible to find infinitely many points, not all on a line, with this property.
J V Narlikar Director, Inter-University Centre for Astronomy & Astrophysics Ganeshkhind, Post Bag 4 Pune 411 007, India Ph - 91-212-351414 and 359415 Fax - 91-212-356417 E-mail: [email protected]
A Burning Question
You are given two non-identical, nonuniform laces. Each takes one hour to burn. Being non-uniform, equal lengths don’t burn in equal times. How will you burn them to determine a time interval of 45 minutes ? A more difficult variation on this: You now have only one such lace. How will you burn it to determine only 15 minutes ? __________________________________________________________________________
70
RESONANCE ⎜ March 1998
Related Documents
Measuring Distances
November 2019 14
Paul A
April 2020 12
Selections From Paul Johnson
October 2019 17
Problem-a
November 2019 34
Problem A
June 2020 21