How to Determine a Line = to Square Root of 3 Geometrically

Step-by-Step Guide

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   Step 1: Get to know the image you'll be creating.

   Both top and bottom, with straight lines will form two equilateral triangles, one atop the other, the bottom one an inverted mirror image of the top triangle.
   
   All the radii are equal and all sides being equal, these are proven equilateral triangles. , The length of this line equals the square root of
   3. , Where the perpendicular cuts the original given unit line to the line's left (or right) endpoint is a distance of .5
   -- let us call this distance a. a^2 = .25.
   
   The hypotenuse has a length of 1; let us call the hypotenuse c and c^2 =
   1. c^2
   - a^2 = b^2 = 1
   - .25 = 3/4 and the square root of this is sqrt(3)/2 and equals 1/2 the dropped perpendicular between the intersection points, top and bottom, of the two circles.
   
   Therefore twice this distance, or the measure of the full perpendicular between the circle's intersection points, equals sqrt(3)/2 * 2 which = the square root of 3 ... the very distance which was sought to be determined geometrically. , Sqrt(3) =
   1.73205080756888 and we can see the black line is about 2*.85 or
   1.7 units in length, roughly. , For more art charts and graphs, you might also want to click on Category:
   Microsoft Excel Imagery, Category:
   Mathematics, Category:
   Spreadsheets or Category:
   Graphics to view many Excel worksheets and charts where Trigonometry, Geometry and Calculus have been turned into Art, or simply click on the category as appears in the upper right white portion of this page, or at the bottom left of the page.
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   Step 2: Make a given finite blue horizontal line of unit length = 1

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   Step 3: and treating each endpoint as the center of a radius

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   Step 4: make two overlapping circles.

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   Step 5: Connect the endpoints of the original line (radius) from either side with the intersection point of the two circles.

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   Step 6: Drop the connecting perpendicular between the top intersection point of the two circles and the bottom intersection point of the two circles.

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   Step 7: Do the math.

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   Step 8: The black line equals the square root of 3 relative to the radius of 1 between 0 and +1 on the x axis.

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   Step 9: Make use of helper articles when proceeding through this tutorial: See the article How to Create a Spirallic Spin Particle Path or Necklace Form or Spherical Border for a list of articles related to Excel

10. 10

    Step 10: Geometric and/or Trigonometric Art

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    Step 11: Charting/Diagramming and Algebraic Formulation.

Detailed Guide

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