Greetings,
Mathematics is a good subject to be "neutral" and is good to be neutral sometimes.
Today, we will speak and introduce the Geometric Figure called "The Astroid". The word "Asteroid" have it origin in the "Astroid".
What is an Astroid? ... What type of figure is? ... What property has? ... What is the formula to draw it? ...
The Astroid may be defined in several modes.
It is the envelope of a straight line, two marked points on which slide along two fixed, mutually perpendicular axes.
To built the figure, you can draw two circles, where the radius of the small is 1/4 the radius of the Big. Then, rolling the small on the Big, we will get the following figure,
The Astroid is the Internal figure in Red. Because our assumption or reduction to choose r=1/4 R, is for this figure, in general we have,
Because write the formula in HTML is not too easy for long formulae, I am leading you to page 222 of the book, Heinrich Dorrie - 100 Great Problems of Elementary Mathematics. Problem #52 (page 231 of the PDF file, page 222 of the book)
(Click to read the book)
# This type of figures is called hypocycloid and in the case, x^{2/3}+y^{2/3}= a^{2/3}
You can read a proof in the book.
I want know to lead your attention to the figure built with the astroid. A so-called, Astroid Diamond,
Now, I will leave this small lesson with a question.
What relation exist between the Astroid Diamond and The Flower of Life?
The Solution is not elementary, but easy after all.
Hint:
Look the Blue or Brown or Green Area.
The Solution is the following. If you consider the Astroid Diamond and rotate it 45°. Or simply add the oval in the figure below to the Astroid Diamond, you will get the "Flower of Life".
I want to end this lesson, with the collection of "Sacred Geometry" figures,
They all are connected with FTHumanEvolutionCourse logo,
Web-Bibliography is:
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