I heard about about Phytagoras Tree, Möbius Strip, and Hypercube along ago while I streamed my mathematic books, but instead of looking to the physical visualization, I enjoyed exploring the equation.
Then I found a blog about mathematic while exploring the tumblr, called VisualizingMath. It gave information about how the equation work and visualized in picture. And they provide the posters of famous mathematic object.
The Möbius strip or Möbius band (UK /ˈmɜrbiəs/ or US /ˈmoʊbiəs/; German: [ˈmøːbi̯ʊs]), also Mobius or Moebius, is asurface with only one side and only one boundary component. The Möbius strip has the mathematical property of being non-orientable. It can be realized as a ruled surface. It was discovered independently by the German mathematicians August Ferdinand Möbius and Johann Benedict Listing in 1858In mathematics,
E8 is any of several closely related exceptional simple Lie groups, linear algebraic groups or Lie algebras ofdimension 248; the same notation is used for the corresponding root lattice, which has rank 8. The designation E8 comes from the Cartan–Killing classification of the complex simple Lie algebras, which fall into four infinite series labeled An, Bn, Cn, Dn, andfive exceptional cases labeled E6, E7, E8, F4, and G2. The E8 algebra is the largest and most complicated of these exceptional cases.
In geometry, a hypercube is an n-dimensional analogue of a square (n = 2) and a cube (n = 3). It is aclosed, compact, convex figure whose 1-skeleton consists of groups of opposite parallel line segmentsaligned in each of the space’s dimensions, perpendicular to each other and of the same length. A unit hypercube’s longest diagonal in n-dimensions is equal to .
The Pythagoras tree is a plane fractal constructed from squares. Invented by the Dutch mathematics teacher Albert E. Bosman in 1942, it is named after the ancient Greek mathematician Pythagoras because each triple of touching squares encloses a right triangle, in a configuration traditionally used to depict the Pythagorean theorem. If the largest square has a size of L × L, the entire Pythagoras tree fits snugly inside a box of size 6L × 4L. (wikipedia)