GC-09 Divide Line In Any Number of Segments

This exercise demonstrates how to divide a line segment in any desired partitions:

Needed analogue tools:

• Dividers

• Pencil

• Straight Edge

• Eraser

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Given:

• Line A-B

Desired:

• Line H-I

Note: in this particular example, I'll divide Line A-B in 5 equally-spaced segments.

1. Draw a straight line starting from A in a similar fashion as shown. Direction and length are per your choice.

2. Draw another straight line starting from B but in a direction opposite to, and parallel to the line in Step 1.

3. Using the dividers, split the line in Step 1 in 5 equal sections by marking the points c, d, e, f. A-c=c-d=d-e=e-f.

4. In a similar fashion, divide Step 2-line in 5 equal sections, whose lengths are the same as the ones we created in Step 4, i.e. A-c=B-g, c-d=g-h, d-e=h-i, e-f=i-j.

5. Using a straight edge, connect the dots in the following manner:

   1. c-j

   2. d-i

   3. e-h

   4. f-g

6. The line segments just created (Step 5) intersect Line A-B at 4 locations:

   1. k

   2. l

   3. m

   4. n

7. Thus, distance A-B=A-k + k-l + l-m + m-n + n-B and A-k=k-l=l-m=m-n=n-B.

If circumstances requires it to divide the line in 2 segments:

• simply connect c with g. Line A-B will be intersected by c-g at its midpoint (that of Line A-B).

If 3 segments are required:

• connect c with h, d with g, intersecting A-B at 2 locations, trisecting A-B.

This method can be applied for any number of desired divisions of a straight line.

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You can download the GH file here:

09_Divide_Line_In_Any_Number_Of_Segments

.zip

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