Is an Apollonian Gasket a shape?
In mathematics, an Apollonian gasket or Apollonian net is a fractal generated by starting with a triple of circles, each tangent to the other two, and successively filling in more circles, each tangent to another three. It is named after Greek mathematician Apollonius of Perga.
Who proposed the Apollonian problem?
Newton
Newton formulates Apollonius’ problem as a problem in trilateration: to locate a point Z from three given points A, B and C, such that the differences in distances from Z to the three given points have known values.
What is Apollo ness theorem?
In geometry, Apollonius’s theorem is a theorem relating the length of a median of a triangle to the lengths of its sides. It states that “the sum of the squares of any two sides of any triangle equals twice the square on half the third side, together with twice the square on the median bisecting the third side”.
What is the difference between Apollonian and Dionysian?
Apollo represents harmony, progress, clarity, logic and the principle of individuation, whereas Dionysus represents disorder, intoxication, emotion, ecstasy and unity (hence the omission of the principle of individuation).
How do you construct a circle tangent to three circles?
Construct the radical center of the three circles, and from that point, draw a line to each of the three poles. In this case, each line intersects its respective circle at two points. The six intersection points are points of tangency for two solution circles, with three tangent points on each solution.
Which is the ratio of the circumference of any circle to the radius of the circle?
two 𝜋 to one
In its simplest form, the ratio of the circumference of a circle to its radius is two 𝜋 to one. For every one unit of radius, there is two 𝜋 units in the circumference.
Where is Apollonius theorem used?
Apollonius’ Theorem is a theorem in elementary geometry, similar to Pythagoras Theorem. It is useful to calculate the lengths of a median of a triangle. It is equivalent to the Parallelogram Law, as stated before.
What is Apollonius theorem formula?
Apollonius theorem also known as Median of a triangle theorem states that in triangle ABC, if AB, BC and AC are the sides and AD is the median to BC, then AB2 + AC2 = 2 (AD2 + BD2).
What is Apollonian and Dionysian examples?
All types of form or structure are Apollonian, thus, sculpture is the most Apollonian of the arts, since it relies entirely on form for its effect. Rational thought is also Apollonian since it is structured and makes distinctions. Drunkenness and madness are Dionysian All forms of enthusiasm and ecstasy are Dionysian.