In the Euclidean geometry, squaring the circle is a term that has been used for different types of long-standing mathematical puzzles that were proved impossible later in the 19th century.
Squaring the Circle is used as a symbolic representation in Alchemy, particularly during the 17th century and since has gained a metaphorical meaning, which depicts attempting anything that may seem impossible.
Mathematics and Geometry
According to some of the famous mathematician, squaring the circle is a term which means constructing a perfect circle and the square with the same area as that of the circle.
The trick for doing the same is precision and accuracy using only a compass and straight edge. This particular assembly of drawing may seem simple from the naked eye but it is very difficult to draw when one takes up the initiative.
A lot of emphases has to be laid on the fine details of drawing the square and the circle because both of these figures should have the same area.
The following lines give a glimpse about the fine details which is required for drawing this particular symbol:
First of all, we are not saying that a square of the equal-area does not exist. If the circle has area A, then a square with side square root of. A has the same area. Secondly, we are not saying that it is impossible since it is possible, but not under the restriction of using only a straightedge and compass.
“is the challenge of constructing a square with the same area as a given circle by using only a finite number of steps with a compass and straightedge. More abstractly and more precisely, it may be taken to ask whether specified axioms of Euclidean geometry concerning the existence of lines and circles entail the existence of such a square.”
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Meaning of Squaring the Circle in Alchemy
The symbol of a circle which is inscribed within a square along with a triangle within a larger circle began to be used somewhere in the 17th century for representing the Alchemy and also the Philosopher’s Stone. This particular stone is considered to be the ultimate goal of Alchemy.
The Philosopher’s Stone, which was sought for various centuries was considered to be an imaginary substance in which various alchemists believed in which had the mind-boggling power of changing any type of metal into precious metals like gold and silver.
Various illustrations are present which include the process of the square in the circle design like the one which is mentioned in Michael Myers’s book Atlanta Fugiens.
This particular book was first published in the year 1617 and narrates the story of a man who is seen using a compass for drawing a circle around another circle which is inscribed within a square along with a triangle.
We can also see that within the smaller circle, a man and a woman are standing who are considered to be the two halves of nature, who are supposedly brought together by the almighty through the process of Alchemy.
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Philosophical Meaning of Squaring the Circle
The philosophical and spiritual meaning of squaring the circle has been described in various religious books and even in different mathematical books.
In terms of spirituality and philosophy, to square, the circle means to see equally in all the four directions and also to treat everyone with equal respect.
By looking in all the four directions equally, that is, up, down, in and out, it gives a complete and wholesome feeling to the individual and makes his or her mind free and liberated.
The circles are often considered to be the symbolic representation of the spiritual mind because they are considered to be infinite and have no end just like the mind which is considered to be an infinite ocean of thoughts.
The square, on the other hand, is considered to be a symbolic representation of the material because the number of physical things which are present in this world comes in the number of 4 like the four seasons, four directions and also the four physical elements which are air, fire, earth, and water.
All this is mentioned in the ancient Greek philosophers writing Empedocles. One has also mentioned about the solid appearance of this particular symbol in various writings and scriptures.
The union of a woman and a man in the Alchemy is considered to be the merging of the physical and spiritual natures. The triangle is also considered to be a symbol of the resulting union of the body, soul, and the mind of both these individuals.
Somewhere around the 17th century, squaring the circle was not yet been proved impossible by various scholars. But it was considered to be a puzzle which was solved by no one and also the solution for the same was unknown.
The concept of Alchemy was viewed very similarly and related to it because it was considered something which was seen by very few and had never got fully completed.
The study of the concept of Alchemy was believed to be about the journey of the individual to understand the concept of God and also the concept of squaring the circle.
People believe that the study of Alchemy was much more about the journey as the finite goal, as no one in this world would ever be able to able to forge a Philosopher’s Stone.
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Metaphorical Meaning of Squaring the Circle
It should always be understood that no one has achieved the task of squaring the circle. This explains its use as a metaphor that has the real meaning to attempt to complete a task, which is seemingly impossible to do.
The comparison of such a task is drawn with finding world peace.
Squaring the circle is considered to be different on the metaphor of attempting to fit a square peg into a perfectly round hole, which is considered to be significant of two inherently incompatible things.
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Alchemy Symbolism
The symbol of a circle, which is inscribed within a square, which is further inscribed within a triangle and then within a circle started somewhere around the 17th century.
Squaring the circle was considered to be a symbolic representation of the process of Alchemy and also the Philosopher’s Stone which is considered to be the ultimate goal of Alchemy.
A lot of illustrations are present on various online platforms and different types of books about the same. The most famous illustrations present in the famous book of Atlanta Fugiens which was written by Michael Maier in the year 1618.
A lot of people in the world have tried to draw this particular figure but were not able to perform it with complete accuracy and precision.
The circles are believed to be a spiritual representation of the mind. This is because the mind is considered to be something that does not have any boundaries and can think to an infinite extent which is similar to a circle with no endings.
The combination of the figures of the triangle, circle, and square is believed to be a reunion of the mind, body, and soul of an individual which helps in achieving the wisdom and knowledge and remaining on the right track and path in life.
The study of all these figures and Alchemy is believed to be much about the journey of the human being and also the goal that one cannot Forge a Philosopher’s Stone.
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Conclusion
Squaring the circle is a term that is related to the Euclidian Geometry where a circle is inscribed within a square. Both of these figures have the same area. It is believed to be a theoretical concept that is almost impossible to attain in the practical sense.
This figure is also related to the concept of Alchemy, where the circle is considered to be the representation of the mind as both these do not have any end or limit. It is believed to unite the mind, body, and soul of the individual.
People Also Ask (FAQs)
What is the origin of Euclidean Geometry?
The Euclidean geometry is believed to be originated from the Greek mathematician Euclid, which he has described in the textbook of geometry. He has deduced several important theorems and propositions from the same which are being used till the present years.
Who is considered to be the father of Geometry?
Euclid, who is also famous all around the world by the name of Euclid of Alexandria is considered to be the father of Math’s and Geometry. His ideas and propositions in the field of math’s are extensively being used from the past many centuries all around the world.
How can we find the area of a square inscribed in a circle?
We can find the area of the square by writing down the side length of the square. The side length of the square is also equal to the diameter of the circle. Half the diameter is the radius, so divide the side length by 2 to get the radius of the circle. Once you know the radius of the circle, find its area.