A dumb adult !!

[lrubin28]

Now I wish I learned my math 30 years ago!!! I need to make a device and maybe the best way to explain this is as a math problem. I have 2 rods, each the same length of 18 inches. If I cross 1 rod over the other I can create 2 isosceles triangles opposite from each other. If I cross them in the middle (9 inches on both rods), I understand that the bases of the triangles that are opposite each other should be the same length. But if I cross the rods further down (say 3 inches on both rods), still creating isosceles triangles opposite each other, the lengths of the 2 bases will be different. I am looking for the formula that lets me calculate the bases. I hope my explantaion made sense....

(what I am trying to make is a measuring device, so that I can measure between the 2 points of the base on one end and the other end will automatically be twice as long, three times as long etc...used for enlarging drawings...hopefully that makes sense too!)

Larry

 

[soroban]

Hello, Larry!

So we have a pair of equal rods fastened together like a pair of scissors.

You already know the base case.
If the pivot is at the middle of the rods, the two bases are equal.
Their ratio is 1:1.

      : - 1 - :
      *       * -
       \     /  :
        \   /  1/2
         \ /    :
          *     -
         / \    :
        /   \  1/2
       /     \  :
      *       * -
      : - 1 - :

If the pivot is at the 1/3 mark,
. . the bases are in the ratio 1:2.

      : - 2 - :
      *       * -
       \     /  :
        \   /  2/3
         \ /    :
          *     - 
         / \   1/3
        * - *   -
        : 1 :

If the pivot is at the 1/4 mark,
. . the bases are in the ratio 1:3.

      : - 3 - :
      *       * -
       \     /  :
        \   /  3/4
         \ /    :
          *     - 
         / \   1/4
        *   * - -
        : 1 :

Got the pattern?

For the ratio \(\displaystyle 1:n\), divide the rods into \(\displaystyle n+1\) parts.
. . and place the pivot at the first mark.


This works for whole-number enlargements: 1-to-5, 1-to-8, etc.
If you want fractional ratios, like 1-to-1.5 (that is, 2-to-3),
. . ask again, okay?

 

[lrubin28]

Thanks very much for the answer! I understand the pattern. I am curious about "why" though...Is there a something you can point me to that explains it (I'm just curious)....thanks again for your help....

Larry

 

[Deleted member 4993]

The ""how" comes from Euclid - theorems of similar triangles.

For two similar triangles - the corresponding sides are proportional.

When you make that "X" - you are making two similar triangles (including the base ).