120! (factorial) Triangle
120! (factorial) triangle without the last 28 zeros. Totaling digits = 783.
Select image to see another triangle with Equilateral Triangles and Equidistant Sequences for 668.
The triangle above shows the first 171 digits of 120! (factorial). The final 28 zeros are removed, elsewise, there would be a total of 199 digits in 120!. There are three clear instances of 668 (in red) that can be seen in the triangle.
If you have ever wondered how many other equilateral triangles can be found within the above triangle or any other similar type of triangle, use the following formula:
The triangle above shows the first 171 digits of 120! (factorial). The final 28 zeros are removed, elsewise, there would be a total of 199 digits in 120!. There are three clear instances of 668 (in red) that can be seen in the triangle.
If you have ever wondered how many other equilateral triangles can be found within the above triangle or any other similar type of triangle, use the following formula:
n * (n-1) * (n+1) * (n+2) / 24
'n' represents the total number of vertices along the base of the triangle. In the above case, there are 19 vertices. Using the given formula with n = 19 will result in a solution of 5985 equilateral triangles available in the above triangle.
All 715 Equilateral Triangles within the 11-vertices-based triangle. By Dan Thomasson
Check out the above illustration. The triangle shows all 715 possible equilateral triangles at the same time. Using the same formula as before, n = 11 results in a solution of 715 total equilateral triangles. I used this triangle to develop my seven-volume puzzle book series called Search for E. T. (Equilateral Triangle). Try out a free online flipbook called Numbers. Solutions are in the back.
Three Stars of David
Three Stars of David in middle of 715 Equilateral Triangle Solutions. By Dan Thomasson
Look closely at the image above. It is slightly blurry being enlarged from the center of the 715 equilateral triangle solution image previously shown on this page. Look closely at the image to see three overlapping Stars of David crosses.
The image below is the same as the image above except that I included a thin outline of the three Stars of David for better viewing. Notice that there are 12 larger star-like shapes directly surrounding all three Stars of David. There are seven larger star-like shapes over and around each individual Star of David [777]. The three Stars of David represent the Trinity of the Father (God), the Son (Jesus), and the Holy Ghost (Spirit).
Three Stars of David outlined in middle of 715 Equilateral Triangle Solutions. By Dan Thomasson
Notice the little triangle in the middle of the three Stars of David. It is the only triangle that is the overlapping of all three Stars of David at the same time. I call this triangle the Thrown of God. Everything else radiates away from this triangle. Check out the following hexagrams: Star of David and Seal of Solomon.