Monthly Archives: March 2013

Lets Get Started!

Welcome to the 345Project!  The purpose of the 345project is to give students the opportunity to totally stump your “educators”.  How many times have you wanted to outsmart your teacher?  Now you can do this with a simple 345 triangle.

A 345 triangle is right triangle with sides of 3 4 and a hypotenuse of  5.

The facts that the 345 triangle presents are so basic it is disturbing that we don’t know this from grade school.  These relationships raise more questions than answers.  If you are asking questions, it means you are curious.  And that is the 345project’s simple goal:  to increase young student’s curiosity.

The choice is yours; you can continue below and step out of your “regularly scheduled” education or just close this window and open your school text book; that’s ok too, your choice!

Students:  Follow the steps below and once you have seen the results for yourself, go to your science/math/history teacher and ask him/her to derive the radius of the earth and moon in miles from a 345 triangle.

Go to your history teacher, and him/her to derive a side of the Giza pyramid (with correct angles) from a 345 triangle.

Once the teacher fumbles and fails, use the steps you learned below to demonstrate this basic information.

When completed, if they mention that the numbers are not exact, ask them what kind of grade you would receive if your average was 99.97%.  If they say it is coincidence, then it is their choice to believe that, but you can always dig deeper.

Teachers/Parents: If you have been queried by curious thinking students with the above questions, ask yourself, why you were not taught this information.  Ask how something so simple, can integrate so many subjects (algebra, geometry, history, geography, biology etc.. the best way to teach) has been left out of ALL educational materials.

You can do this on a single sheet of graph paper to get a basic drawing, if you go bigger, it is easier to be more accurate.

Tools needed: Graph paper, compass, ruler.  If you are in a class room just use a ruler and free hand the circles.  You will be creating the logo of this site!

  1. Draw a 345 triangle it the upper left hand side, with the 3 side vertical, and the 4 side horizontal the hypotenuse is 5.  Thanks Pythagoras!  A^2 + b^2 = c^2  :  3^2 + 4^2 = 5^2 :  9 + 16 = 25!
  2. Create a square using the 3 unit length side of the triangle.
  3. Mirror the 345 triangle on the other side of the square.
  4. The total length of the 2 triangles and the square bottom lines combined is 11.  Complete a 11 x 11 square below the 2 triangles and 3×3 square.
  5. Create a circle in the smaller 3×3 square, by drawing lines from each corner to the opposite corner.  The point where they cross is the center of the square.  Make a circle using the compass, so the radius is from the center to the edge of the square.  The edge of the circle should touch the square at the top, right, bottom and left.
  6. Repeat number 5, for the large 11 x 11 square.   ( you have just drawn 2 circles that demonstrate the proper proportion of the earth to the moon)
  7. Every circle has 360 degrees.  Multiply 360 x 3 = 1080  Radius of the moon in miles= 1079.6, 1079.6/1080 =  99.96%
    Multiply 360 x 11 = 3960  radius of earth in miles = 3956.6 , 3956.6/3960 =  99.91% accurate.


Extra credit! The great Giza Pyramid:

  1. Draw a horizontal line through the center point of the large earth circle connecting to each side of the square.  (should be where the circle touches the square on the left and right)
  2. Draw a line from the point on the side of the square to the center point of the moon.
  3. Repeat 2 for the other side.
  4. You have just drawn an accurate representation of the side of the Giza pyramid in Egypt.  Not that the angles of the bottom sides are close to 51 degrees.

Extra credit! Circle and square with same perimeters:

  1. Draw a circle with the same perimeter as the 11 x 11 square.  This measurement is difficult to calculate but easy to create using the 345 method.
  2. Put the anchor of your compass in the center of the earth circle, extend the pen to the center of the moon circle, rotate 360 degrees.
  3. Because pi is a not an integer (transcendental), the accuracy is not exact but within 99%.


Have fun with this.  School your teachers!  Here are some links from where I learned this.  Dig Deeper and question your educators!!