Beauty In Mathematics
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© Ogan Gurel
Beauty in Mathematics Ogan Gurel, MD The mathematicians’ patterns, like the painter’s or the poet’s, must be beautiful; the ideas, like the colours or the words, must fit together in a harmonious way. Beauty is the first test: there is no permanent place in the world for ugly mathematics. G. H. Hardy as imagination bodies forth The forms of things unknown, the poet’s pen Turns them to shapes, and gives to airy nothing A local habitation and a name.
Shakespeare, A Midsummer-Night’s Dream
Everything from Nothing Area of mathematics Set Theory
Example / result
Theorem
Physical example
Derivation of natural numbers from the empty set
Number Theory
Fundamental Theorem of Arithmetic Euclid’s proof of the Infinitude of Primes Rational and irrational numbers
Pythagorean proof of the incommensurability of root 2
Fibonacci Numbers & the Golden number Real Analysis
The construction of the real numbers
Algebra
Solving equations; implications for number
Petal arrangements Countability of the naturals and nondenumerability of the continuum
Complex numbers
Fundamental Theorem of Algebra
Encompasses, e, pi, i, 1, addition, and multiplication ... all leading back to 0
Euler’s Formula
© Ogan Gurel
The universe of symmetry Symmetry denotes that sort of concordance of several parts by which they integrate into a whole. Beauty is bound up with symmetry. H. Weyl Area of mathematics
Example / result
Set Theory
Empty set as embodying the most symmetry
Group Theory
Definition of Symmetry
Theorem
Physical example Before the Big Bang
Symmetry operations and symmetry elements Platonic Solids Euclidean Group
Ornamental Symmetry and the planar Fedorov groups (17).
Broken symmetry Topology
Clathrin-coated pits
From the Big Bang onwards
Polyhedra
Euler’s Theorem
Topological equivalence & topological invariants
Jordan separation theorem
Cell membranes and protein synthesis
All is wave Symmetry denotes that sort of concordance of several parts by which they integrate inot a whole. Beauty is bound up with symmetry. H. Weyl Area of mathematics
Example / result
Trigonometry
Translation of angular measures into linear measures
Group Theory
Definition of Symmetry
Theorem
Physical example
Symmetry operations and symmetry elements Platonic Solids Euclidean Group
Ornamental Symmetry and the planar Fedorov groups (17).
Broken symmetry Topology
Clathrin-coated pits
From the Big Bang onwards
Polyhedra
Euler’s Theorem
Topological equivalence & topological invariants
Jordan separation theorem
Cell membranes
Beauty in Mathematics Ogan Gurel, MD The mathematicians’ patterns, like the painter’s or the poet’s, must be beautiful; the ideas, like the colours or the words, must fit together in a harmonious way. Beauty is the first test: there is no permanent place in the world for ugly mathematics. G. H. Hardy as imagination bodies forth The forms of things unknown, the poet’s pen Turns them to shapes, and gives to airy nothing A local habitation and a name.
Shakespeare, A Midsummer-Night’s Dream
Everything from Nothing Area of mathematics Set Theory
Example / result
Theorem
Physical example
Derivation of natural numbers from the empty set
Number Theory
Fundamental Theorem of Arithmetic Euclid’s proof of the Infinitude of Primes Rational and irrational numbers
Pythagorean proof of the incommensurability of root 2
Fibonacci Numbers & the Golden number Real Analysis
The construction of the real numbers
Algebra
Solving equations; implications for number
Petal arrangements Countability of the naturals and nondenumerability of the continuum
Complex numbers
Fundamental Theorem of Algebra
Encompasses, e, pi, i, 1, addition, and multiplication ... all leading back to 0
Euler’s Formula
© Ogan Gurel
The universe of symmetry Symmetry denotes that sort of concordance of several parts by which they integrate into a whole. Beauty is bound up with symmetry. H. Weyl Area of mathematics
Example / result
Set Theory
Empty set as embodying the most symmetry
Group Theory
Definition of Symmetry
Theorem
Physical example Before the Big Bang
Symmetry operations and symmetry elements Platonic Solids Euclidean Group
Ornamental Symmetry and the planar Fedorov groups (17).
Broken symmetry Topology
Clathrin-coated pits
From the Big Bang onwards
Polyhedra
Euler’s Theorem
Topological equivalence & topological invariants
Jordan separation theorem
Cell membranes and protein synthesis
All is wave Symmetry denotes that sort of concordance of several parts by which they integrate inot a whole. Beauty is bound up with symmetry. H. Weyl Area of mathematics
Example / result
Trigonometry
Translation of angular measures into linear measures
Group Theory
Definition of Symmetry
Theorem
Physical example
Symmetry operations and symmetry elements Platonic Solids Euclidean Group
Ornamental Symmetry and the planar Fedorov groups (17).
Broken symmetry Topology
Clathrin-coated pits
From the Big Bang onwards
Polyhedra
Euler’s Theorem
Topological equivalence & topological invariants
Jordan separation theorem
Cell membranes
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