File Name: mathematics in nature space and time .zip
- What's the Universe Made Of? Math, Says Scientist
- The Mathematics of Minkowski Space-Time
- Mathematical Physics 2 Pdf
- The Nature of Space and Time
What's the Universe Made Of? Math, Says Scientist
On the contrary Mathematics is quite interesting and is present in many aspects of life and anybody can study and understand mathematics if one believes in oneself. In fact mathematics is a whole cortical-skill-subject that involves words, lines, logic, patterns, symmetry, rhythm, space, association and the over-riding concept of fun. The author endeavors to justify his claim in the following pages.
Scientists do not study nature just because it is useful: they study nature because it is beautiful. If nature were not beautiful, it would not be worth knowing. And if nature were not worth knowing, life would not be worth living. We cannot understand nature if we do not first learn the language and grasp the symbols in which it is written.
There is nothing in our lives, in our world, in our universe, that cannot be expressed with mathematical theories, numbers, and formulae. Mathematics is the key to understanding our world around us. It is perhaps the purest of the pure mental endeavor of humankind.
Mathematics has been called the mother of all sciences; to me it is the backbone of all systems of knowledge. Mathematics is a tool that has been used by man for many years. It is a key that can unlock many doors and show the way to different logical answers to seemingly impossible problems. Not only can it solve equations and problems in everyday life, but it can also express quantities and values precisely with no question or room for other interpretation.
There is no room for subjectivity. Though there is a lot of mathematics in politics, there is no room for politics in mathematics. Mathematics is not fundamentally empirical —it does not rely on sensory observation or instrumental measurement to determine what is true. Indeed, mathematical objects themselves cannot be observed at all!
Richard Feynman. If you want to learn about nature, to appreciate nature, it is necessary to understand the language that she speaks in. It is the science of patterns and order and the study of measurement, properties, and the relationships of quantities; using numbers and symbols.
Patterns are result of naturally occurring processes. One of the purposes of natural science is to build models of these processes, the complexity arises from simplicity. From rainbows, river meanders, and shadows to spider webs, honeycombs, and the markings on animal coats, all these patterns can be described mathematically. Fact of creation: Some living beings which even do not have a brain perfectly perform so complicated tasks as not to be accomplished even by human beings.
The honeycomb is hexagonal in shape because a hexagon is the most appropriate geometric form for the maximum use of a given area and also the hexagonal structure provides the maximum strength. The honey bees need not go to a school to learn this.
Area of a single cell square units equilateral triangle square hexagon 0. The red space between cells depicts the wasteful area for a square and a hexagonal construction. A hexagonal structure also provides the maximum strength.
Although the wax cell walls may be only about 0. Considering that for each gram of wax produced the bee needs to consume 6 - 7 grams of honey, it is to the bees' advantage that the shape providing the maximum area has the minimum expenditure of materials and energy. Though they start from different places, the bees, great in number, construct identical hexagons and then weave the honeycomb by combining these together and meeting in the middle.
The junction points of the hexagons are assembled so deftly that there is no sign of their being subsequently combined. The compound eyes of insects typically exhibit hexagonal packing schemes.
No doubt the same criteria of maximizing light-sensitive area coverage while minimizing the volume of inert edge- cell material that are familiar from honeycombs apply here. Patterns can be constructed by distributed intelligence: Termites build castles with similar complexity to human buildings.
There is no plan, there is no blueprint. No foreman organizes the work of workers and no one governs the workers. The termite mound is built by self organized efforts. The Fibonacci numbers are Nature's numbering system.
The Natural sequence is formed by adding a succeeding number to the previous root number, and is as follows: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, … and so on. This ratios approaches phi, the golden number an irrational number. They appear everywhere in nature, from the leaf arrangement in plants, to the pattern of the florets of a flower, the bracts of a pinecone, or the scales of a pineapple.
The original problem that Fibonacci investigated in the year was about how fast rabbits could breed in ideal circumstances. He has a newly-born pair of rabbits, one male, one female, and he puts them in a BIG cage. Rabbits are able to mate at the age of one month so that at the end of its second month a female can produce another pair of rabbits. Suppose that our rabbits never die and that the female always produces one new pair one male, one female every month from the second month on.
The puzzle that Fibonacci posed was How many pairs will there be in one year? Suppose that when a plant puts out a new shoot, that shoot has to grow two months before it is strong enough to support branching.
If it branches every month after that at the growing point, we get the picture shown above. Honeybees, Fibonacci numbers and Family trees The genealogy of the bee is a pattern. This pattern is the result of pathogenesis, the development of an unfertilized egg into an adult animal without fusion with sperm. The queen bee mates only once.
She can then produce either unfertilized eggs or fertilized eggs. The unfertilized eggs become male drones, while the fertilized eggs become female workers or queens.
In other words, a female bee has two parents, and a male bee has only one parent; a female. Female bees reproduce by parthenogenesis during the spring and summer.
In the fall, the eggs produce both males and females. These insects mate, and the females produce fertilized eggs that hatch in the spring. Family Tree of Drone Bee He had 1 parent, a female. He has 2 grand-parents, since his mother had two parents, a male and a female. He has 3 great-grand-parents: his grand-mother had two parents but his grand-father had only one.
A Golden spiral is formed on a golden rectangle as below. Take any two numbers at random, second bigger than the first such as and 2. Add them together 3. Add the result to the second largest number 4. Repeat from step 2 for a while five or six times, maybe 5.
Divide the last result you got by the second-to-last result I'll bet your answer is somewhere close to 1. This also gives the best possible area exposed to falling rain so the rain is directed back along the leaf and down the stem to the roots. For flowers or petals, it gives the best possible exposure to insects to attract them for pollination. Nature uses spirals to prevent overcrowding. The Fibonacci numbers, golden ratio or divine proportion , and the golden spiral are therefore applicable to the growth of every living thing, including a single cell, a grain of wheat, a hive of bees, sea shell, plants, and even all of mankind.
The DNA molecule, the program for all life, is based on the Golden section. It measures 34 angstroms long by 21 angstroms wide for each full cycle of its double helix spiral. The DNA cross-section is also based on Phi. A cross-sectional view from the top of the DNA double helix forms a decagon: A decagon is in essence two pentagons, with one rotated by 36 degrees from the other, so each spiral of the double helix must trace out the shape of a pentagon. So, no matter which way you look at it, even in its smallest element, DNA, and life, is constructed using phi and the golden section!
When the distance between the navel and the foot is taken as 1 unit, the height of a human being is equivalent to 1. The Sarva Dharm Symbol is based on pentagon. While heartbeats vary, some believe that a heartbeat that reflects this perfect phi relationship represents a state of being that is one of health, peace and harmony.
Perfect breathing The breath moves in and out in the geometry of perfect damping, or the perfect way to approach the icy stillness of oneness. The depth and the duration of each adjacent breath get smaller by ratio PHI golden mean. Phi appears in the Solar System and The Universe From the distances between the planets, to the structure of Saturn's rings to the shape of the Universe itself, phi is found again and again in different manifestations.
New findings reveal that the universe itself is in the shape of a dodecahedron, a twelve-sided geometric solid with pentagon faces, all based on phi. Saturn's magnificent rings show a division at a golden section of the width of the rings.
Curiously, even the relative distances of the ten planets and the largest asteroid average to phi. There's even an unusual energy source at the frequency of phi that is found in the universe.
The Mathematics of Minkowski Space-Time
In Stephen W. Hawking and Roger Penrose gave a series of public lectures on general relativity at the Isaac Newton Institute for Mathematical Sciences at the University of Cambridge. From these lectures, published this year by Princeton University Press as The Nature of Space and Time, Scientific American has culled excerpts that serve to compare and contrast the perspectives of the two scientists. In particular, Hawking and Penrose disagree on what happens to the information stored in a black hole and on why the beginning of the universe differs from the end. The black hole will evaporate in the process, so that ultimately perhaps nothing of the original mass will be left. But during their formation, black holes swallow a lot of data—the types, properties and configurations of the particles that fall in. Although quantum theory requires that such information must be conserved, what finally happens to it remains a topic of contentious debate.
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It seems that you're in Germany. We have a dedicated site for Germany. Authors: Catoni , F. Hyperbolic numbers are proposed for a rigorous geometric formalization of the space-time symmetry of two-dimensional Special Relativity. The system of hyperbolic numbers as a simple extension of the field of complex numbers is extensively studied in the book. In particular, an exhaustive solution of the "twin paradox" is given, followed by a detailed exposition of space-time geometry and trigonometry. Finally, an appendix on general properties of commutative hypercomplex systems with four unities is presented.
Download PDF. Platonic Solids' and 'Rhythm and Cycles'. Includes full colour illustrations and diagrams throughout. A resource for Steiner-Waldorf teachers for.
Mathematical Physics 2 Pdf
Includes full colour illustrations and diagrams throughout. A resource for Steiner-Waldorf teachers for maths for Class 7 age and Class 8 age Excellent option for courses covering more theory than practice and a lot of 2-D NMR.
Mathematical Physics 2 Pdf Physics Courses. The book bridges the gap between an introductory physics course and more. The AP Physics 1 and 2 Course and Exam Description, which is out now, includes that curriculum framework, along with a new, unique set of exam questions.
But what if the universe itself is math? That's what cosmologist Max Tegmark believes. In Tegmark's view, everything in the universe — humans included — is part of a mathematical structure. All matter is made up of particles, which have properties such as charge and spin, but these properties are purely mathematical, he says. And space itself has properties such as dimensions, but is still ultimately a mathematical structure.
Сьюзан в испуге взглянула на Хейла. Он стоял с безучастным видом, словно происходящее его никак не касалось.
The Nature of Space and Time
Что ты говоришь. Расскажи это Чатрукьяну. Стратмор подошел ближе.
- У тебя есть ключ от кабинета Фонтейна. - Конечно. Я же его личный помощник.
К черту кодекс чести, - сказала она. - Посмотрим, чем ты тут занимаешься. Окинув быстрым взглядом находящееся за стеклом помещение шифровалки, Сьюзан включила кнопку яркости. Вспыхнувший экран был совершенно пуст. Несколько этим озадаченная, она вызвала команду поиска и напечатала: НАЙТИ: СЛЕДОПЫТ Это был дальний прицел, но если в компьютере Хейла найдутся следы ее программы, то они будут обнаружены.
sumwnwzhnlgdlige - Listen, read and download John Blackwood's book Mathematics in Nature, Space and Time in PDF, EPub, Mobi, Kindle online. Free book.
Говорите. - Где мой ключ? - прозвучал знакомый голос. - Кто со мной говорит? - крикнул Стратмор, стараясь перекрыть шум. - Нуматака! - огрызнулся сердитый голос. - Вы обещали мне ключ.
Я не собираюсь оплачивать твое пристрастие к наркотикам, если речь идет об. - Я хочу вернуться домой, - сказала блондинка. - Не поможете .
Наконец-то, подумал пассажир такси. Наконец-то. ГЛАВА 77 Стратмор остановился на площадке у своего кабинета, держа перед собой пистолет. Сьюзан шла следом за ним, размышляя, по-прежнему ли Хейл прячется в Третьем узле. Свет от монитора Стратмора отбрасывал на них жутковатую тень.
Я хотел уйти с сознанием, что добился своей цели. - Но вы добились своей цели, - словно со стороны услышала Сьюзан собственный голос, - Вы создали ТРАНСТЕКСТ.