These Are the Biggest Numbers in Mathematics Counting to three is so easy, a salamander can do it. Seriously. Lab experiments have shown that captive salamanders are able to distinguish between piles of two fruit flies and piles of three. If you're not impressed, we understand. A human being who'd never taken a single math class would have no trouble doing the same thing. Yet as numbers grow bigger, our ability to comprehend their values starts to break down. Billions, Trillions and Quadrillions By the commonly accepted definition we use today, one billion is equal to a thousand millions. Note that a trillion is written as a one followed by twelve zeroes. Now take a pen, grab some paper, and write down a nice, tidy row of 100 individual zeroes. And Then Your Mind Blows... The number's size will blow your mind. Enormous as a Googol is, at least you can write it down numerically. 1010100 (or 10 to the 10th to the 100th) And if you think a Googolplex is big, get a load of Skewes' number, which looks like so:
Sunyata (Emptiness) in the Mahayana Context 1. Sunyata (Emptiness) is the profound meaning of the Mahayana Teaching. Two thousand five hundred years ago, the Buddha was able to realise "emptiness" (s. sunyata). By doing so he freed himself from unsatisfactoriness (s. dukkha). From the standpoint of enlightenment, sunyata is the reality of all worldly existences (s. dharma). It is the realisation of Bodhi — Prajna. There are two ways for us to understand this concept of sunyata in the Mahayana context. Mahayana teachings have always considered that the understanding of sunyata is an attainment which is extremely difficult and extraordinarily profound. For example, in the Prajna Sutra it says "That which is profound, has sunyata and non-attachment as its significance. Again in the Dvadasanikaya Sastra (composed by Nagarjuna, translated to Chinese by Kumarajiva A.D. 408) it says: "The greatest wisdom is the so-called sunyata." 2. The sutras often use the word "great void" to explain the significance of sunyata. 3. 4. 5.
Homeomorphism - Encyclopedia of Mathematics A one-to-one correspondence between two topological spaces such that the two mutually-inverse mappings defined by this correspondence are continuous. These mappings are said to be homeomorphic, or topological, mappings, and also homeomorphisms, while the spaces are said to belong to the same topological type or are said to be homeomorphic or topologically equivalent. They are isomorphic objects in the category of topological spaces and continuous mappings. A homeomorphism must not be confused with a condensation (a bijective continuous mapping); however, a condensation of a compactum onto a Hausdorff space is a homeomorphism. The term "homeomorphism" was introduced in 1895 by H. A second problem is the topological characterization of individual spaces and classes of spaces (i.e. a specification of their characteristic topological properties, formulated in the language of general topology, cf. References How to Cite This Entry: Homeomorphism.
What Mathematics Reveals About the Secret of Lasting Relationships and the Myth of Compromise In his sublime definition of love, playwright Tom Stoppard painted the grand achievement of our emotional lives as “knowledge of each other, not of the flesh but through the flesh, knowledge of self, the real him, the real her, in extremis, the mask slipped from the face.” But only in fairy tales and Hollywood movies does the mask slip off to reveal a perfect other. So how do we learn to discern between a love that is imperfect, as all meaningful real relationships are, and one that is insufficient, the price of which is repeated disappointment and inevitable heartbreak? Making this distinction is one of the greatest and most difficult arts of the human experience — and, it turns out, it can be greatly enhanced with a little bit of science. She writes in the introduction: In the first chapter, Fry explores the mathematical odds of finding your ideal mate — with far more heartening results than more jaundiced estimations have yielded. Fry explains: She breaks down the equations:
Pali Middle Indo-Aryan language native to the Indian subcontinent Burmese Kammavaca manuscript written in Pali in the 'Burmese' script. Pali () is a Middle Indo-Aryan liturgical language native to the Indian subcontinent. Origin and development[edit] Etymology[edit] The word 'Pali' is used as a name for the language of the Theravada canon. The name Pali does not appear in the canonical literature, and in commentary literature is sometimes substituted with tanti, meaning a string or lineage.[3]: 1 This name seems to have emerged in Sri Lanka early in the second millennium CE during a resurgence in the use of Pali as a courtly and literary language.[4][3]: 1 As such, the name of the language has caused some debate among scholars of all ages; the spelling of the name also varies, being found with both long "ā" [ɑː] and short "a" [a], and also with either a retroflex [ɭ] or non-retroflex [l] "l" sound. Geographic origin[edit] Early history[edit] Manuscripts and inscriptions[edit] T. According to K.
Klein bottle Non-orientable mathematical surface The Klein bottle was first described in 1882 by the mathematician Felix Klein. The following square is a fundamental polygon of the Klein bottle. The idea is to 'glue' together the corresponding red and blue edges with the arrows matching, as in the diagrams below. This immersion is useful for visualizing many properties of the Klein bottle. The Klein bottle, proper, does not self-intersect. Suppose for clarification that we adopt time as that fourth dimension. Like the Möbius strip, the Klein bottle is a two-dimensional manifold which is not orientable. Continuing this sequence, for example creating a 3-manifold which cannot be embedded in R4 but can be in R5, is possible; in this case, connecting two ends of a spherinder to each other in the same manner as the two ends of a cylinder for a Klein bottle, creates a figure, referred to as a "spherinder Klein bottle", that cannot fully be embedded in R4.[5] with itself. Simple-closed curves [edit]
Did artists lead the way in mathematics? Mathematics and art are generally viewed as very different disciplines – one devoted to abstract thought, the other to feeling. But sometimes the parallels between the two are uncanny. From Islamic tiling to the chaotic patterns of Jackson Pollock, we can see remarkable similarities between art and the mathematical research that follows it. The two modes of thinking are not exactly the same, but, in interesting ways, often one seems to foreshadow the other. Does art sometimes spur mathematical discovery? Patterns in the Alhambra Consider Islamic ornament, such as that found in the Alhambra in Granada, Spain. In the 14th and 15th centuries, the Alhambra served as the palace and harem of the Berber monarchs. It’s a triumph of art – and of mathematical reasoning. It’s also possible to combine different shapes, using triangular, square and hexagonal tiles to fill a space completely. An emotional experience? The patterns are not merely beautiful, but mathematically rigorous as well.
Mahayana Mahāyāna (Sanskrit: महायान mahāyāna, literally the "Great Vehicle") is one of two (or three, under some classifications) main existing branches of Buddhism and a term for classification of Buddhist philosophies and practice. The Buddhist tradition of Vajrayana is sometimes classified as a part of Mahayana Buddhism, but some scholars may consider it as a different branch altogether.[1] According to the teachings of Mahāyāna traditions, "Mahāyāna" also refers to the path of the Bodhisattva seeking complete enlightenment for the benefit of all sentient beings, also called "Bodhisattvayāna", or the "Bodhisattva Vehicle The Mahāyāna tradition is the largest major tradition of Buddhism existing today, with 53.2% of practitioners, compared to 35.8% for Theravāda and 5.7% for Vajrayāna in 2010.[3] Etymology[edit] The earliest Mahāyāna texts often use the term Mahāyāna as a synonym for Bodhisattvayāna, but the term Hīnayāna is comparatively rare in the earliest sources. History[edit] Origins[edit]
Manifold Topological space that locally resembles Euclidean space In mathematics, a manifold is a topological space that locally resembles Euclidean space near each point. More precisely, an -dimensional manifold, or -dimensional Euclidean space. The concept of a manifold is central to many parts of geometry and modern mathematical physics because it allows complicated structures to be described in terms of well-understood topological properties of simpler spaces. Manifolds can be equipped with additional structure. The study of manifolds requires working knowledge of calculus and topology. Motivating examples [edit] The top and right charts, and respectively, overlap in their domain: their intersection lies in the quarter of the circle where both -coordinates are positive. , though differently. can be constructed, which takes values from the co-domain of back to the circle using the inverse, followed by back to the interval. , then: It can be confirmed that x2 + y2 = 1 for all values of s and t. since . .
Pi and the Great Pyramid It was John Taylor who first proposed the idea that the number &pi might have been intentionally incorporated into the design of the Great Pyramid of Khufu at Giza. He discovered that if one divides the perimeter of the Pyramid by its height, one obtains a close approximation to 2&pi. He compared this to the fact that if one divides the circumference of a circle by its radius, one obtains 2&pi. He suggested that perhaps the Great Pyramid was intended to be a representation of the spherical Earth, the height corresponding to the radius joining the center of the Earth to the North Pole and the perimeter corresponding to the Earth's circumference at the Equator. It is true that if one divides the Great Pyramid's perimeter by its height, one indeed obtains a very good approximation to 2&pi. How can one calculate the probability that an architect building a pyramid would choose a slope which is so close to 4/&pi? 1. 2. 3. 4. 5. 1. 2. But what Herodotus actually wrote is quite different.