Doing what seems impossible – part 1

Would it be possible to create a square from a circle with only a compass and ruler, having exactly the same surface? Can a circle be squared?

Doing what seems impossible – part 1

Words that contain the letters ‘qua’ such as quarter, and quartet, refer to the Latin word quadratus, which means square. This problem: the quadrature, ‘squaring’ a circle, has been an obsession of mathematics for thousands of years.


It was formulated as a riddle for the first time by the oracle of Delphi.

This oracle was the highest aspect of the deity from that time. Philosophers from ancient times studied the coherence and spacial relations of our universe. In doing so, they used numbers, forms and formulas, not only as quantities, such as we do nowadays, but as living symbols giving insight into the cosmos, life and the human state of being. These were means with which they tried to understand the incomprehensible, thus trying to approach the divine – with the help of intuition and logical thinking.

Many free spirits have attempted to solve this issue.

All his life, Leonardo da Vinci was obsessed by the transformation of forms. He scribbled, drew and he alone already found 169 formulas for the squaring of the circle.

However, not one of them solved the problem. It remained an unsolved, impossible puzzle.

In his book ‘the magical powers of nature’ Karl von Eckhartshausen writes about the squaring of the circle:

It seems to be resisting the nature of things if one thinks that quadrating means: representing a circle by a square?  The riddle appealed to me, stayed with me and surprised me.

I hear Hermes say in my mind:

Let yourself be penetrated by the thought that nothing is impossible for you, consider yourself immortal and capable of understanding everything, the nature of all that lives.

The impossible is simply a possibility that you do not yet understand.

Why would you want to turn a circle into a square with the same surface area? It seems so nonsensical. Why search for the philosopher’s stone? Perform alchemy to turn base metal into gold? Yet it has always fascinated scientists and mystics alike how forms, substances and bodies can undergo transformations. With its riddle, the oracle of Delphi calls for abstract thinking, for looking into the world of the spirit. Then the square stands for material power, for time – timeliness, impermanence and form. The circle for infinite liveliness of becoming, of eternity.

God made eternity, eternity the world, the world carries its time, the time its generations, a teeming multitude of myriads of beings, from human to celestial,

we read in the Corpus Hermeticum of Hermes Trismegistos. The core force of the divine descends, incarnates in the form. Thus everything carries within itself the essence, the core of God. Heaven, in the earth. From infinitely great, to the invisibly small and never anything is lost. The law of conservation of energy prevails throughout the universe. Where then do you find the equality of opposites? Of time and eternity, square and circle, two extremes? The oracle gave two tools: compass and ruler.

I see before me how in the Middle Ages God was represented with compasses in hand when creating the world. How William Blake, Newton paints with compasses, how in Freemasonry compass and yardstick are important attributes. With the ruler you find the center in the square by drawing diagonal lines in the circle. With a compass, you construct an equilateral triangle inside the circle by setting the radius of the circle against the circumference. The riddle is not just about circle and square, it finds its solution using the triangle and the center found. They slide together to form the Rosicrucian symbol of circle, triangle, square and the point at the center.

You calculate the area or circumference of a circle using the irrational number pi.
Rational numbers are natural, whole numbers or integers, such as 1, 2, 3…, with which we can count. They can also be expressed as a fraction of two integers. A fraction like ½ clearly indicates half, ¼ a quarter. A characteristic of an irrational number is that it cannot be expressed as a fraction of integers and that the number of decimal places is infinite. Irrational numbers are “unnameable” or “unpronounceable,” they cannot be pronounced with that infinite series of decimal places, they can only be described as the action that forms them, such as “the square root out of two. It is a number that keeps reaching for eternity. Pi is often rounded to 3.14. The discovery of irrational numbers presented mathematicians with philosophical questions regarding the earth and the universe. To what reality do irrational numbers actually belong?

It is now known that the riddle of “squaring a circle” can indeed be solved by an approximation with rational numbers. We also say a transcendental number. The word ‘transcendent’ touches on an inner experience, it enters our world of experience. It carries something of movement. Transcendence means “transcending” or “climbing”. The action contained in a transcendent number is about rising above everyday reality so that we experience a higher reality – something of the great mystery of life. Overwhelming and fascinating are the laws of the universe – the divine plan hiding in it, longing to reveal itself! The irrational number symbolizes the point at the center of circle and square, the one point from which transcendence is possible, unreal to the world because it transcends the earthly, but for spiritual seekers the highest reality.

There an unearthly, infinite power flows into the heart, from where it leads the mind towards the spirit.

Behold now – through me- the world that shows itself to you, 

as Pymander (that is: the Mind) says to Hermes,

and take deep within you how beautiful it is: a pure and imperishable body, internally strong and young, and ever increasing in strength.

See also the seven fundamental worlds, formed according to an eternal order, which together, each according to its own course, fulfill eternity. See, how everything carries the One within it. See, how everything is full of soul, everything is full of light, with no fire anywhere. For love and the fusion of opposites and of dissimilarities have become light, radiating through the revealing power of God, the creator of all good….

Consider now through me the world that shows itself to you. Discover in the pure Mind the fire of God that lifts every law of nature. The holy triangular fire of wisdom, love and deed that ignites in your heart. Water cleanses, fire changes and unites. Squaring the circle means allowing inner transformation, from transforma, transcending form, to trans-figura, trans-figuration. Through the spiritual fire, everything becomes one luminous life. All in all, you are a whole, complete and free human being. Do what seems impossible.


(To be continued in part 2)

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Date: August 14, 2023
Author: Ankie Hettema-Pieterse (Netherlands)
Photo: Caroline Hernandez on Unsplash

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