Galois Automorphism
Oil on canvas
80 cm x 60 cm
Price: 3.418 EUR Sold
In geometry, this is a type of bijective map that preserves the algebraic structure of a field. Here is the process observed through the movement of triangles in parallel planes. Galois automorphisms are important in Galois theory, which is a branch of algebra that examines the relationship between field extensions and groups.
Hilbert’s Twenty-First Problem
Oil on canvas
50 cm x 70 cm
Price: 3.294 EUR Sold
The parallel postulate, which is related to Hilbert’s 21st problem, is often used in the study of triangles to prove results such as the sum of the interior angles of a triangle.
Euler’s Inequality
Poncelet’s Porism
Oil on canvas
70 cm x 50 cm
Price: 3.162 EUR Sold
Price: 3.173 EUR
Euler’s inequality is a fundamental result in geometry that applies to triangles where the sum of the squares of the lengths of the sides of a triangle is greater than or equal to four times the square root of three times the area of the triangle.
According to Poncelet’s porism, if two triangles are such that each has an incircle that is tangent to all three sides of the triangle, then any circle that is tangent to one of the triangles’ incircles is also tangent to the other triangle’s incircle.
These works are a part of the math-art project “The Power of a Triangle”. The triangle is the only plane figure described by a finite number of straight-line segments where all dots are directly connected. Out of all polygons, only a triangle is always rigid.
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