Master stonemason and sculptor Ina Michalski from Weimar has entitled her ensemble of figures made from Anröchter green limestone “Wa(a)gnis Geometrie”. The platonic bodies made of stone with steel unfoldings, our sculpture(s) of the month for February 2016, refer us to the exciting relationship between mathematics and art. What do aesthetics have to do with numbers, you might ask. A lot, would be the answer. Symmetries, proportions and perspectives play a major role in art.
Master stonemason and sculptor Ina Michalski from Weimar has entitled her ensemble of figures made from Anröchter green limestone “Wa(a)gnis Geometrie”. The platonic bodies made of stone with steel unfoldings, our sculpture(s) of the month for February 2016, refer us to the exciting relationship between mathematics and art. What do aesthetics have to do with numbers, you might ask. A lot, would be the answer. Symmetries, proportions and perspectives play a major role in art. Just think of the “golden ratio” as the epitome of harmony and beauty – a division ratio originating from the geometry of the philosopher Euclid (around 300 BC), in which the ratio of the whole to its larger part corresponds to the ratio of the larger to the smaller part. The “golden ratio” was and is used in architecture, painting and even sculpture (e.g. by Leonardo da Vinci, Albrecht Dürer and Le Corbusier).
With her Platonic Bodies, Ina Michalski embarked on a journey into the universe of geometry, in particular through the fascinating worlds of Max Bill’s three-dimensional sculptures. “His works, which are largely based on mathematical-geometric principles, became a source of inspiration for me,” says the artist. The elegance, clarity and structure of the five Platonic solids captivated her during her research. Her artistic interpretation made from Anröchter green limestone makes mathematics, but also beauty in art and nature, tangible, even tangible. The individual sculptures weigh between 100 and 250 kilograms and are each 45 centimetres high. The corresponding steel unfoldings roll out the sides of the bodies two-dimensionally. They act like a mirror image, revealing the innermost parts of the figures. They were spot-welded, treated with salt to give them a rusty look and then oiled. “Over 500 hours of work went into this ensemble,” says Michalski. An intensive examination of shapes and proportions as a source of human inspiration and aesthetic perception.
What is the mathematical background to the five Platonic solids – which are named after the philosopher Plato because of his written treatises on them? They are the only shapes that are composed of perfectly regular polyhedra (three-dimensional solids) bounded by polygons (polygons) as lateral surfaces. Their names go back to the Greek numbers and denote the number of their respective faces: the tetrahedron (four equilateral triangles), the hexahedron (six squares), the octahedron (eight equilateral triangles), the dodecahedron (twelve regular pentagons) and the icosahedron (20 equilateral triangles). All faces of the respective solid have the same edge lengths, i.e. they are equiangular and equilateral, which in turn means that the faces are congruent to each other. In addition, each corner of the solid has the same distance from the center. Due to this absolute symmetry, there is an outer, edge and inner sphere. In addition, they are convex, i.e. there are no reentrant corners and edges. All these conditions exist in their entirety only in the five Platonic solids, which is mathematically proven by Euler’s polyhedron theorem.
These geometric conditions are impressive. The Platonic solids appear perfect: There is no flaw attached to the solids, they are self-contained and perfect. Rational and functional. The artist Max Bill formulated the principle: “Beauty from function and as function”. Ina Michalski also sees this trait embodied in her sculptures. However, another aspect must be added to geometric beauty or beautiful geometry. Nature also follows mathematical laws. For example, the arrangement of hydrogen atoms in the sp³-hybridized methane hybrid orbital corresponds to a tetrahedron. Various crystal or molecular compounds occur in this form. Mathematics permeates reality, forming the essential elements of existence. Is art then a reflection of nature? Or does art distort reality with the help of its own structures and laws? Is mathematics above all else or is it merely a means of interpretation? These are the questions posed by Ina Michalski’s Platonic solids. Whether they also give us an answer is something everyone has to decide for themselves.
In any case, Ina Michalski can imagine her sculptures in a school playground. Pupils could thus be taught a certain branch of geometry didactically, as all the components of the Platonic solids can be experienced visually and empirically. Geometric art as an aid to understanding, sculptures to illustrate abstract laws, but also mirrors of nature or simply aesthetics to touch and experience. The sculptures make clear what connects mathematics, art and nature. They make it possible to experience what often only happens unconsciously within us. Be it when listening to music, which we humans usually only like when we hear mathematically well-structured sequences of notes. Or when we perceive faces as beautiful because they are symmetrical.
The philosopher Immanuel Kant characterized beauty as a “subjective generality”. It is based neither on a subjective judgment of taste, which can turn out differently for everyone, nor on a universally valid judgment of reason, which should be rationally comprehensible to everyone. Beauty is somehow accessible to everyone, but it is also not completely comprehensible according to laws. With regard to our sculpture(s) of the month, one could say that it is not their mathematically perfect execution alone that constitutes their essence, but something else that is not so easy to get to the point or the number. Perhaps there is a basic mathematical sense in our nature, but this, or in other words the “pure function”, does not yet explain our aesthetic sensibility. Or does it? Immerse yourself in the sculptural world of Platonic solids and let yourself be inspired!
Find out more about the artist here.
