Twinkle Twinkle Little Pyramid Star
Part II
©Lorena Loo
Part II
©Lorena Loo
© Copyright Lorena Loo
Creating a Golden Pyramid Using Fibonacci Numbers & A Square Grid
Step 1: Start with a square grid. Here I use a 26x26 square grid with the center marked by the gold dot. Draw a line of length 13 units on the grid and mark off the 5 unit point. That creates a line of 13 units in length and subdivided into 5 and 8 units. 5, 8 and 13 are the 5th, 6th and 7th Fibonacci numbers.
Step 2: If you think of the east as the direction in which the initial line was drawn in step 1, then repeat step 1 for each of the other three compass directions.
Step 3: Now draw a square of sides of lengths 10 units, 5 units on either side of the red lines in the grid and centered about the gold dot.
Step 4: Join the endpoints of the sides of the square to the endpoint of the corresponding red line as illustrated in the diagram. All you need to do is fold up the figure along the blue lines forming the sides of the square until the apex of your pyramid is directly above the center (gold colored dot) of the square base.
The Golden Pyramid has certain properties true to its name of "Golden" for the Golden ratio or phi crops up in its dimensions as seen in the table below.
The ratios in this chart are exact. That is phi, phi squared and the square root of phi are the exact ratios of the dimensions, even though I have also given the numerical values to 9 decimal places. They were calculated using the three right angle triangles in the pyramid as illustrated below.
Curiously, the Great Pyramid (Cheops) in Egypt is almost exactly a true Golden Pyramid. For further details on this, will be available in my article on The Great Pyramid.
Using the same concepts explored in this article, we can construct three dimensional regular pyramids with regular pentagonal bases, regular hexagonal bases, etc. from two dimensional 5-pointed, 6-pointed, etc. stars.
Using the same concepts explored in this article, we can construct three dimensional regular pyramids with regular pentagonal bases, regular hexagonal bases, etc. from two dimensional 5-pointed, 6-pointed, etc. stars.
Text and images (unless otherwise indicated in the credits) are copyrighted
© by Lorena Loo
In the instances where images in the public domain have been modified as in the case of geometrizing them, the modified images are no longer public domain but the copyright of the author who made the modifications. Here that means me, Lorena Loo. That is by copyright law.
© by Lorena Loo
In the instances where images in the public domain have been modified as in the case of geometrizing them, the modified images are no longer public domain but the copyright of the author who made the modifications. Here that means me, Lorena Loo. That is by copyright law.
