The central sanctuary of Islam, the Kaaba, is located there. Mecca is the birthplace of the Prophet Mohamed. The spiral can also be drawn from the center outward instead of from the outside toward the center. The center point towards which the spiral moves is exactly at the intersection of the diagonals of each of the golden rectangles (mouseover).
The length of the line should correspond to the golden section major of the first line. from the golden section of the line a 90° angle is drawn clockwise.dividing the line in the golden section (blue: golden section major, orange: golden section minor).Drawing a line (lowest horizontal line).The golden spiral is often represented in an approximation construction. five lines).Ī golden spiral occurs when the radius of a circle is shortened by the factor of the golden section when it is rotated about the center every 90°. five corners), a pentagonal star on the other hand is called pentagram (engl. These lines always intersect in the golden ratio (light blue and orange lines).Ī regular pentagon is called pentagon in Greek (engl. If all vertices of a pentagon are connected, five lines are created, which together form a pentagonal star. If these five points are connected, a regular pentagon is created (dark blue lines). through the left point of intersection of the circle with the given line (left yellow point) draw a line from the upper vertex of the pentagon and draw the length of the given line on it (orange point at the bottom left).The radius of the circle is equal to the distance from the golden section of the given line to the center of the line (gray point)
Draw a circle around the center of the given line.The length of the given line is subtracted from this line (orange point at the bottom right). from this upper point a line is drawn through the golden section of the given line (right yellow point).It is rotated upward by the golden section of the given line (right yellow point) until it meets the central perpendicular of the given line (upper blue point) the minor of the golden section of the given line is determined as the radius of a circle.is known by the given distance (left and right black point).Left and right corner point of the pentagon The central perpendicular of the line is also necessary (dashed vertical line). Given is a line, which was divided in the golden section (black horizontal + right yellow point). In a regular pentagon, all sides are of equal length. The golden ratio is necessary to construct a regular pentagon. For geographical classification further places with mouseover The latitude of the pilgrimage city Mecca with the Kaaba, which is important in Islam, is located in the golden section between north and south pole (blue and orange arc). The Fibonacci numbers result from the sum of the numbers that lie on the 45° angle This becomes clearest if the triangle is displayed left-justified instead of centered (mouseover). Pascal's triangle contains the Fibonacci sequence. The relationship between Fibonacci numbers and the golden ratio The pattern of the golden angle can be found, among others, in composite flowers (Mouseover)
What initially appears chaotic develops into a multi-armed spiral (here 13 arms). Every 137.5 degrees, an increasing colored dot is placed on an increasing radius. Illustration of the golden angle of 137.5°. It has its origin at the intersection of the diagonals of the largest surrounding golden rectangle (mouseover) Construction of the golden section according to the method of the ancient mathematician Euclid into a given line of length 1.Ī golden rectangle is created when the smaller part of the golden section is rotated by 90° (mouseover)įor the construction of a regular pentagon the central perpendicular and the golden section of a line are neededĪpproximation construction of the Golden Spiral.
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