Parallel postulate

At the time most mathematicians were trying desperately to prove Euclid 's fifth postulate as derived from other axioms. We now know that in fact this can not be done as it must be taken as an axiom to define a Euclidean space. This postulate, reformulated in modern terms, reads as “given a line and a point not on it, one can draw through the point one and only one coplanar line not intersecting the given line.” [8] Meanwhile a different idea occurred to Lobachevsky. Instead of trying to prove the fifth postulate he imagined a system where the fifth postulate was different. Instead of specifying only one line being parallel to the original passing through some point, Lobachevsky imagined a space where infinitely many lines could pass through such a point and be parallel to the first line. Today we call this hyperbolic geometry and can imagine it as a saddle shaped space. [4] This convex space has some fascinating properties, such as all “triangles” having their angles add up to less than 180 degrees. Following some exploration Lobachevsky concluded that his newly devised geometry was in fact consistent with all other postulates in Euclid’s elements. He thus concluded that Euclidean geometry is a specific case and there are other, more general geometries. Although published in 1826 these ideas did not become widely accepted until long after Lobachevsky’s…

I used to believe that geometry wasn’t possible without algebra, that geometry was essentially a representation of algebra. I didn’t have an experience of geometry that focused on the creativity and ingenuity that I’ve come to now know. Chapter 6 of Journey Through Genius reiterates how impressive the discipline of geometry truly is. Cardano’s solution to the general solution was astonishing, to me, because of the literal use of geometry to find the appropriate algebraic identities and the…

I used the parallel format to restate and summarize these same points in the conclusion. For example, I started my speech asking how many people had heard of the quote and ended the presentation by bringing that same idea back into the conclusion. I also made sure to restate the ideas in my thesis and my specific speech purpose from the introduction in the conclusion. Throughout the entire speech, I made sure to explain to the audience what I was about go talk about or go over, making my topic…

The movie industry in India is definitely undergoing changes to cater to modern mindsets of younger generation who are more liberalized. In the past, movies tend to be portrayed more stereotypes such as gender, storytelling and culture. However, with revolutions in the information and communications technology, Indian movies are becoming more diasporic, taking into account the audiences outside India. Hence, this idea intrigued us into the issue of stereotypes and if any changes in the…

YOUNGER AGE GROUP 2) Social Interactions/ Development : EJ : Male: Birthday ( 6/3/2015) EJ a 15 months child seem to be very reserved . He is seen sitting in the corner of the classroom away from his classmates. Therefore, he does not interact much with any of the other children , but rather seeks teh attention of the teachers. When he does not get the attention , he walks away and play s witha toy car. He is participating in solitary play. Solitary play refers to playing alone , without…

Marr’s main prediction was that parallel fiber-to-Purkinje cell synapses were strengthened during learning; in contrast, Albus postulated that the parallel fiber-to-Purkinje cell synapses would weaken (he also thought they could strengthen and that the parallel fiber-to-stellate cell synapses were also modifiable.) Albus defended his synaptic weakening argument by pointing out that the parallel fibers should be trained to emulate the post-complex spike pause and not the excitatory phase of the…

The influence of Bollywood in everyday life According to the Oxford Dictionary, the name ‘Bollywood’ is actually derived from a portmanteau of Bombay and Hollywood; which we all popularly know as the hub of the American film industry. India, the world’s largest producer of films actualizes an average of 1,288 to 1,500 feature films every year compared to films produced by Hollywood which are only a fraction. Although Hindi cinema is just a segment of India’s annual film production, it remains…

company was a hardware firewall provider. Upon my investigations, I came to the understanding that their parallelization was not effective at all. In a standard test of their performance, before I provide my algorithm, they could process six million packets per second throughput; But, it was just normal packet filter with barely even header inspection, also refreshing the new rules took approximately three minutes and forty-five seconds, that was their time to generate new rules. The task of…

Bollywood divas that rule 2016 Bollywood is the general term for the Hindi language film industry situated in Mumbai. The entire Indian silver screen is generally alluded to the world standards with the expression of “Bollywood”. Moreover, Bollywood is one of the biggest film makers in India, which holds the most astounding records in Box Office collections. Naturally, acting is the most important domain of this industry where the works of the actors and actresses are viewed through any…

hierarchical domain decomposition method, were already able to analyze three dimensional models defined by meshes, of arbitrary shape, with hundreds of million Degrees Of Freedom (DOF) cite{Ogino-2005}. More recently, explicit particles methods, parallelized by DD strategies, were also able to perform simulations of very large models: in 2014, Murotani et al. cite{Murotani-2014a}, using a two level voxel-based domain decomposition to parallelize explicit MPS, performed tsunami simulations…