How to Use Random Cut Theorem and Simple Probability

Step-by-Step Guide

1. 1

   Step 1: Learn or recall from "Elements"

   Grab/copy the yellow and orange diagram from this page onto the Clipboard.
   
   TYpe Command and c for copy to make a copy of the diagram.
   
   At the Desktop, click on the XL icon on the Dock to start Excel.
   
   Open a New Workbook in Excel.
   
   Holding down the Shift Key, do Edit Paste Picture into a new worksheet.
   
   Save the file under an appropriate filename into a logical folder, and make notes from the steps below, below the diagram.
2. 2

   Step 2: Book II

   Stated another way, if x = y+z, then x^2 = (y+z)^2 = y^2 + 2yz + z^2.
   
   In the diagram then, square HF = y^2, square CK = z^2, rectangle AG = yz and rectangle GE = yz as well. ,,, where the next random event will be.
   
   There is a .3 * .7 = 21% chance the next event will be in one of the two rectangles, and so a 42% chance it will be in either rectangle (or in 2yz).
   
   There is a .3 *.3 = 9% chance the next event will be in square CK (or in z^2).
   
   There is a .7 * .7 = 49% chance the next event will be in square HF (or in y^2). (.42 + .09 + .49 =
   1.00 = 100% chance there will be a next event (presumably).
   
   This is an important assumption and not always the case.
   
   Or perhaps it's a presumption.
   
   It's in the sump somewhere, speaking etymologically ... , It's still very usable information today.
   
   A random cut of a card deck, a random cut in an accident, a random cut in Nature, etc., etc.
   -- all subject to analysis because of Euclid. , For more art charts and graphs, you might also want to click on Category:
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3. 3

   Step 3: Proposition 4

4. 4

   Step 4: that "If a straight line be cut at random

5. 5

   Step 5: the square on the whole is equal to the squares on the segments and twice the rectangle contained by the segments."

6. 6

   Step 6: Learn or recall that

7. 7

   Step 7: per the above diagram

8. 8

   Step 8: if segment AC = x and segment CB = y

9. 9

   Step 9: that (x+y)^2 also equals x^2 + y^2 + 2xy.

10. 10

    Step 10: Call the Area of the Whole square AE equal to 1 or 100% Probability.

11. 11

    Step 11: Guesstimate from the random cut in the diagram that it occurred at a value of .70 of length AB.

12. 12

    Step 12: Calculate from your guesstimate what a dart's chance's of landing in each square are

13. 13

    Step 13: or where the next robbery will be

14. 14

    Step 14: It's important to remember that Euclid solved this about 2.300 years ago!

15. 15

    Step 15: Make use of helper articles when proceeding through this tutorial: See the article How to Describe a Square on a Given Line AB for a list of articles related to Euclid

16. 16

    Step 16: Geometric and/or Trigonometric Art

17. 17

    Step 17: Charting/Diagramming and Algebraic Formulation.

Detailed Guide

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