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The Golden Mean and Nature’s Mandalas

The Golden Mean and Nature’s Mandalas

Author: K S

Students will explore how the Golden Mean connects with the patterns, which are found in the  organic shape of a Mandala

This tutorial explores the patterns from nature which is created through the phenomenon of the Golden Mean. Examples of a mandala can be seen in the pattern in a nautilus shell, or the seed pod of a sunflower.

Students will:

  1. Investigate the connection between the Golden Mean and  patterns of organic shape
  2. Construct original artwork using the formula of the Golden Mean. patterns of organic shape
  3. Collaborate to summarize  and problem-solve concepts


This tutorial integrates Mathematics and Visual Art, but the initial concept can be adapted to fit every content area. The golden mean is also known as called the golden ratio, the golden rectangle, and the golden section. Other names include extreme and mean ratio, medial section, divine proportion, divine section, golden proportion, golden cut, golden number, and mean of Phidias.

Architects and artists proportion their works to approximate the golden ratio, specifically in the form of the golden rectangle, in which the ratio of the longer side to the shorter is the golden ratio. The golden ratio has been used to analyze the proportions of man-made systems, such as financial markets.

Philosophers and spiritualists regard this “rule of thirds” as an ancient science, which explores and explains the energy patterns that create and unify all of creation; their focus concentrates on the precise way that the energy of Creation organizes itself.


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The Mathematical Formula of Organic Shape

Source: The Lesson Planet

Love's Divine by Seal

“Many people say that it is beauty alone that draws them to music. But great music brings us even more. By providing the brain with an artificial environment, and forcing it through that environment in controlled ways, music imparts the means of experiencing relations far deeper than those we encounter in our everyday lives. When music is written with genius, every event is carefully selected to build the substructure for exceptionally deep relations. No resource is wasted, no distractions are allowed. Thus, however briefly, we attain a greater grasp of the world (or at least a small part of it), as if rising from the ground to look down upon the confining maze of ordinary existence.”

Robert Jordain, Music, the Brain, and Ecstasy: How Music Captures Our Imagination

Source: Robert Jordain, Music, the Brain, and Ecstasy: How Music Captures Our Imagination