It is an external Circle that equals the Area of the Square, not the Circumscribed! by Giovanni A. Orlando   Written by Administrator Sunday, 23 January 2011 17:38 The Uomo Vitruviano by the Great Leonardo Da Vinci.   Greetings in this very Sun-day of Wisdom and Illumination,     No. There are no Magic ... Just Ignorance and Fear.     To-day was a magic day that bring to me a Good Wisdom about Mathematics.     Leonardo (Da Vinci) ... was right connecting the Circle with the Square and the Golden Ratio, that leads to Φ.     In the past, in the Mediterranean Area, from Italy to Greece to Israel, to Arabia, was common, still to the year 1500, to add the City to the Name of the Person, basically because there were not too much people.    And so, Leonardo is "Da Vinci", because Vinci is the city where he born and Live. Juda Iscariot was so called because Iscariot was the city and Saint Paul was Paul of Tarsus, in Greece.    Well, I want to introduce a Gift that is a Picture ... close to the Leonardo famous picture where you can explain the Circling the Square, as well the Magic of the Great Pyramid that honor pi and connect pi,π with psi, Φ.     I will not be rigorous ... but very clear. You need to understand that Pi, or p is constant.       And therefore two different ratio, for two different circles, with two different circumference, lead to the same number.       At first please consider the Pythagorean Triangle, 3:4:5.       Is clear that the Square has side long 11, and the perimeter is 44. Right?       You can consider the Small Circle Above the Big Circle, like the Moon and the Earth. Like you see the Moon circle has diameter 3 and the Earth Circle has diameter 11. Clear?       Now, you need to draw a Bigger circle than Earth, with the same center but crossing the center of the Moon circle. This is the dotted Circle.       Now this circle, the Dotted has the same Circumference than the Perimeter of the Square.       It is clear? ... Is not immediate.       But the "secret" here is to introduce another Pythagorean Triangle, inside the Earth Circle, which diameter is 2, and which apothem or height is equal to the square root of psi. Of course this is possible because, Φ2=1+Φ     Φ is the Golden ratio, Φ=(1+√5)/2.     Now, we can consider the Pyramid, which proportions ... following the following figure, respect the proportion, h:b =4:π.     If this is "possible", then according to the internal Triangle in the figure, we will have that √Φ:1=4:π.     In some sense the internal triangle has a double, like a raised triangle figuring out a pyramid, as well the triangle that fulfill the equivalence for the calculus of the circumference for the dotted circle.     Now, this proportion, √Φ:1=4:π, lead to us that, √Φ = 4/π, if this is possible, and it is! ... and is clear that perimeter is the Area of the base of the Pyramid, that is squared, and is 44.     Now, because,      π = Cexternal/2 x radiusexternal = 44 (because the area of the square,4x11)/ 2 x 7 = 22/7.     Therefore, we need not purchase expensive books, or take two degrees ... we need simply to remain calm, exercise the mind ... and read the right books.      The original idea arrives to me from the Miranda Lundy - Sacred Geometry, but was Seraphis Bay book, "Dossier on the Ascension" that let me conclude ... and do the math! Thanks, Giovanni A. Orlando. Last Updated on Sunday, 23 January 2011 18:27