Can you divide a line segment into N equal parts where N is a prime number

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matherapist

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Can you divide a line segment into N equal parts where N is a prime number

Given a line segment of length L, divide it into N pieces/parts of length L/N where N is a Prime number. For N=3, this amounts to trisecting the line. You can only use an unmarked straitedge and a compass.

Posted 161 day ago

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Answers (6)

This is a note for matherapist.
Trisecting an angle using Archemedes Spiral is not acceptable, since it would violate the problem statemen that only straightedge and compass should be used and somesort of searching and trial and error is not permited.
Mathematically, it has been proved that trisecting a general angle using straightedge and compass is impossible. Professor rajbaba78.

Posted 160 day ago

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matherapist

Raj,

The question was mainly for students but your answer is correct. However for 4,
I would bisect the nine, and then bisect the half line, and mark this length off on the other end. You can also use this technique to trisect or divide an angle into equal parts using this technique in conjunction with the Archimedes Spiral

Posted 161 day ago

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It does not make any difference if N is prime or not prime. To divide L into say 4 parts (4 is not a prime) draw a line close to L using the tip of L, thus you get an angle. Now:
1- mark 4 equal parts(any size) on the new line.
2- draw a straight line from the last marked point to the end of L. Call this line "M line"(or use any other letter)
3- now from the other marked points, draw additional lins parallel to the M line.
Doing this, your L line will be divided into 4 equal parts. Use the same procedure no matter how many parts you want to have on your Line L.

In this procedure you need the following experties:
a) how to marke equal distances on a line
b) how to draw a line parallel to a given line from given points

This is your answer Given to you by Professor rajbaba78.

Posted 161 day ago

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atta

The length of the line segment L divided into N equal parts where N is a prime number has an infinite number of pieces and parts that divide into the ratio of L/N. Starting with (N = 2), the line segment L is bisetected; with (N = 3)< the line is trisected, etc. What this means is that as the N parts begins to increase, the line L expands into N pieces leaving the ratio of L/N converging to 0.

J.C

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math_fanatic

The answer is yes. If you don't care if the sub-segments' lengths are whole numbers, then this works for any number L that is a positive real number. If you want the lengths of the sub-segments to be whole numbers, then L must be a positive whole number that is a multiple of N.

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samzappala

According to the headline: Can you divide a line segment into N equal parts where N is a prime number.
Any amount can be measured with equal distances. 1,2,3,5,7,11..... are prime numbers.

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