(128) 2. An Euler path is a path that will cross through each edge of a graph exactly once. An Euler path can start at any point and end with a different end point. A graph that has an Euler path can have either zero or two odd vertices, however the rest must be even. An Euler circuit is a circuit that goes through every edge of the graph exactly once.
In other words, a 2-painting of G_6 must contain monochromatic L_3 subgraphs. Ramsey’s Theorem In our problem, we have only considered a particular case of a 2 painting of a graph that has v=R(3,3). This is a singular, very specific case and example of Ramsey’s Theorem. What Ramsey’s Theorem states is that if you have a sufficiently large enough graph and paint it in any amount of k-colours, there must always exist a monochromatic complete subgraph. Before we get to proving Ramsey’s Theorem, we must first completely generalize our previous example and prove the following lemma of painting a graph with 2 colours true: Lemma: An integer R(m,n), m,n ∊ ^+, exists such that any 2-painting of G_(R(m,n)) in the colours c_1,c_2, contains either a G_m with all its edges painted c_1 or a G_n with all its edges painted c_2.
Identity is indicated as E does nothing, has no effect all molecules/objects possess the identity operation, i.e., posses E. E has the same importance as the number 1 does in multiplication (E is needed in order to define inverses). 2. n-Fold Rotations: Cn, where n is an integer rotation by 360°/n about a particular axis defined as the n-fold rotation axis. C2 = 180° rotation, C3 = 120° rotation, C4 = 90° rotation, C5 = 72° rotation, C6 = 60° rotation, etc. Rotation of H2O about the axis shown by 180° (C2) gives the same molecule back. Therefore H2O possess the C2 symmetry element.
Pascal’s triangle is a triangular arrangement of binomial coefficients. It’s is named after French mathematician Blaise Pascal (1623-1662), in the western world. Despite the fact that pascal’s triangle is named after Blaise pascal, other mathematicians from India, Persia (Iran), China, Germany, and Italy knew about and applied their knowledge of the triangle centuries before he was born. Halayudha a 10th century Indian mathematician and commentator gave the first clear description of Pascal’s triangle in his commentary in an ancient Indian book called Chandah Shastra. Not long after that, a Persian poet and mathematician by the name of Omar Khayyam (1048-1131) and a Chinese mathematician by the name of Yang Hui (1238–1298) had both discussed this mathematical triangle and so the triangle is referred to as Khayyam’s triangle in Iran and Yang Hui’s Triangle in China.
To solve quadratic equations by using the factorizing method simply means we need to factorize the quadratic equation. For example: x2 + 3x – 4 is (x+4) and (x−1), simply just arrange it in this form: ax2 + bx + c = 0. Which would be: (x+4) and (x−1) =0 So, x=-4 or x=1 Last but not least, to solve quadratic equations by using the completing square method: • Step 1 Divide all terms by a (the coefficient of x2). • Step 2 Move the number term to the right side of the equation. • Step 3 Complete the square on the left side of the equation and balance this by adding the same value to the right side of the equation.
Benjamin Henry Latrobe: The Man Who Built America, Above & Below Most know Benjamin Henry Latrobe as America’s first professional architect, and the designer of the US Capitol. What many do not know is that among his several architectural achievements, this man also developed a fresh water system in early urban areas from Philadelphia to New Orleans. Biography/Background: Latrobe was born May 1, 1764, near Leeds, England. He attended Moravian schools as a child and later went on to be educated in England and Germany. In school he became fluent in many languages and familiarized himself with the classical arts.
The Blaschke Lebesgue Theorem states that the Reuleaux triangle has the least area of all plane convex sets of the same constant width b. The minimum area is ((π-√3)/2)b2. This theorem was first proved independently by Blaschke. He was the first to demonstrate its constant width properties and the first to use the triangle in numerous real world mechanisms. 5.2 MATHEMATICAL CALCULATION:- 5.2.1 Determination of distance of centre from sides:- AC= s AR=
Therefore, existence is something you think about, not felt or sense about. On numbers, there is obviously no argument against it being an objective construction. But, there are two things to consider, one is what Russell called the propositions of arithmetic (“2+2=4”) and the empirical propositions of enumeration (“I have ten fingers”). Pure mathematics is definitely not derived from perception. “To know that a mathematical proposition is correct, we do not have to study the world, but only the meanings of the symbols.” (p. 177).
Similar to the modern atomic theory, alternating scientific concepts encourage the proposal of new ideas and leading of discoveries based on pre-existing concepts. Not of only scientific but also linguistic, philological, sociological, and philosophical, since all academic fields share the same basis of rationale allowing interconnection to occur. By noting that in science atoms are mostly empty space, and acknowledging that chaos in Greek means “gap” referring to the same empty space, we could define Nietzsche’s anti-conformist Ubermensch commentary “one must still have chaos in oneself to be able to give birth to a dancing star” with greater breadth than as a belief that self-actualization derives from unorganized religion and disorder of moral and ethical codes for the morality police and false virtue are nonexistent; rather, everything is composed of atoms, being empty space and
It was the Egyptians who invented the very first alphabet in about 300 BC, which has been highly influenced for the origin of the English alphabet. In a comparison with the other nations it is envisaged that the history of the alphabet of Sri Lanka goes for years. It has been proved through a research conducted by the former commissioner of archeology Dr. Shiran Daraniyagala that there was a civilization comprised with literacy here in Sri Lanka. This fact was supported by the evidence in a piece of mud pot founded from an excavation in Anuradhapura Athugal Nuwara in which the word “ANURUDA” has been indicated in Aryan Prakrit language (Brahmi) letters somewhere in 500 BC. Those were quit similar to the ancient Indian Brahmi letters.