TikZ Gallery

This is a gallery with most of the mathematical drawings I've ever used on lectures of mine. Most of the files in here are .tikz files containing TikZ code I wrote, but some other files are included too. For further information on how to use the pictures in this gallery and what the licensing terms are please check out the Using This Gallery page.

This picture represents the 26-nodes diagram

26-nodes-diagram.tikz

A visual representation of the Calebi-Yau manifold

This picture represents a complex lattice with two linearly independent periods

complex-lattice.tikz

This picture represents the relationshipt between the real, complex and surreal numbers

complex-surreal-venn.tikz

This picture represents the action of the action of the generators of the Coxerter group of the complete graph of four vertices corresponding to the nodes in a maximal free 3-gon

coxerter-group-reflections.tikz

This picture represents a cube

This picture represents a domond-like thingy

An ilustration of the proof that the representation of the Dihidral group is irreducible

dihedral-representation-is-irreducible.tikz

This picture represents the action of the dihedral group in the real plain

dihedral-representation.tikz

This picture represents the group structure of the points of an elliptic

elliptic-curve-group-structure.tikz

This picture represents the cartesian plain

euclidian-plane.tikz

A plot of the number of topological spaces of n points in logarithmic scale

finite-topological-plot.tikz

This picture represents the lattice antisomorphism between the lattice of the subgroups of the Galois group of a Galois extension and the lattice of intermediary subfields of such extension.

galois-lattice-antisomorphism.tikz

This picture represents the fact that geodesics locally minimize distances

Original artwork by Alexander Grothendieck: the commutative diagram from the Grothendieck-Riemann-Roch theorem, surrounded by fire and two devils carrying forks. Generated with svg2tikz <https://github.com/xyz2tex/svg2tikz> from https://en.wikipedia.org/wiki/File:Grothendieck-Riemann-Roch.jpg

grothendieck-riemann-roch.tikz

A diagram of the classification of finite simple groups in the format of a periodic table

groups-periodic-table.eps

This picture represents the Poincaré disc model of the hyperbolic plane

hyperbolic-plane-disc.tikz

Relief representation of the j-invariant elliptic modular function

The j-invariant Klein function in the complex plane

This picture represents the complete graph of four vertices

Vector graphic illustrating the structure of a Klein bottle, with traced line along the surface

klein-bottle.eps

This picture represents the Mobius strip

This picture represents the first columns of the chacter table of the monster simple group

monster-group-character-table.eps

This picture represents the natural number line

natural-number-line.tikz

This picture represents the ordinal number line

ordinal-number-line.tikz

Shows p-adic closed balls of radii p^(-1) (same hue) and p^(-2) (same colour) for p = 3

This drawing represents the correspondance between conjugation by pure unitary quaternions and rotations in the 3-dimensional euclidian space: the coordinates of a unitary quaternion p number with zero real cofficient induce a line through the origin in the 3-dimensional enclidian space, and conjugation by cos t + p sin t acts as rotation by 2 t around this axis.

quaternion-rotation.tikz

This picture represents the real number line

real-number-line.tikz

This picture represents the relationshipt between the real, ordinal and surreal numbers

real-ordinal-surreal-venn.tikz

This picture is a comparison between the euclian distance and the Riemannian distance in a three-dimensional sphere

riemannian-metric.tikz

This picture represents the fact that reflections are rigid motions

rigid-motion-reflections.tikz

This picture represents the fact that rotations are rigid motions

rigid-motion-rotation.tikz

This picture represents the definition of a smooth map between manifolds

smooth-function.tikz

This picture represents the definition of a smooth manifold

smooth-manifold.tikz

This picture represents the isomorphism between the n-dimensional sphere and the quotient of the (n + 1)-dimensional simple orthogonal group by the n-dimensional simple orthogonal group

sphere-quotient.tikz

This picture represents a three-dimentional sphere

All the Sporadic groups in their subquotient relationship

sporadic-groups.eps

square-to-circle-projection.tikz

square-to-circle-projection.tikz

This diagram represents the relationship between standard number sets

standard-sets-venn.tikz

This picture represents the stereographic projection

stereographic-projection.tikz

Visualization of the surreal number tree

surreal-number-tree.eps

Tally marks: four vertical bars crossed by a single horizontal bar

tally-marks.eps

This picture represents the tangent space at a point in a smooth manifold

tangent-space.tikz

This picture represents a mug continuously morphing into a donut

topology-mug-donut.tikz

This picture represents the universal convering of the unit circle

unit-circle-covering.tikz

This picture represents the unit complex circle

unit-circle.tikz

A graphical depiction of the central projection between the upper semi-sphere and the Euclidean plane: we map each point in the upper half of the sphere to the projection of this point in the tangent plane at the north pole by drawing a line between this point and the center of the sphere and then taking the intersection of this line with the plane.

upper-central-projection.tikz