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Sphere Inside out Part - II

Related:  Matematica

Dimostrazioni matematiche umoristiche [HOME - BASE Cinque - Appunti di Matematica ricreativa] A prima vista possono sembrare errate ma ciascuna di esse contiene un fondo di verità "Un matematico è un congegno che serve a trasformare il caffé in teoremi" Paul Erdos 1. 2. Caso n=1: in un insieme di un solo cavallo, è ovvio che tutti i cavalli di quell'insieme sono dello stesso colore. Caso n=k: supponiamo di avere un insieme di k+1 cavalli. Abbiamo quindi che: se il lemma è vero per k lo è anche per k+1. Quindi tutti i cavalli sono dello stesso colore. 3. 4. Studente di fisica: - Non sono sicuro della validità della tua prova, perciò penso che sia meglio fare un esperimento. Studente di ingegneria: - In realtà non sono sicuro delle vostre risposte. Studente di informatica: - Voi avete avuto l'idea giusta ma ci mettete troppo a concludere. Desidero umilmente ricordare che 1 non è un numero primo. 5. 6. Procediamo per induzione. Se n = 1, allora a, b, essendo interi positivi, devono essere entrambi 1. Keith Goldfarb 7. 8. 9. 10. 11.

Acme Klein Bottle Shap Coordinates: Etymology[edit] Early (12th- and 13th-century) forms such as Hep and Yheppe point to an Old Norse rendering Hjáp of an Old English original Hēap = "heap", (of stones), perhaps referring to an ancient stone circle, cairn, or to the Shap Stone Avenue just to the west of the village. [1] Description[edit] The village has three pubs, a small supermarket, a fish and chip shop, an antique book shop, a butcher's shop, a primary school, a newsagent's, a coffee shop, a ceramic art studio called Edge Ceramics, a fire station, a bank (only open 4 hours a week), a shoe shop (New Balance factory shop) an Anglican church and 3 B&B/ Hostels. Major employers in the area are Hanson and Tata Steel. The civil parish of Shap (formerly Shap Urban Parish) includes the hamlet of Keld and parts of the granite works and limestone works, and has a population of 1,221.[2] The parish shares a joint parish council with Shap Rural. Shap is on the route of the Coast to Coast Walk. Transport links[edit]

K-MODDL > Tutorials > Reuleaux Triangle If an enormously heavy object has to be moved from one spot to another, it may not be practical to move it on wheels. Instead the object is placed on a flat platform that in turn rests on cylindrical rollers (Figure 1). As the platform is pushed forward, the rollers left behind are picked up and put down in front. Is a circle the only curve with constant width? How to construct a Reuleaux triangle To construct a Reuleaux triangle begin with an equilateral triangle of side s, and then replace each side by a circular arc with the other two original sides as radii (Figure 4). The corners of a Reuleaux triangle are the sharpest possible on a curve with constant width. Other symmetrical curves with constant width result if you start with a regular pentagon (or any regular polygon with an odd number of sides) and follow similar procedures. Here is another really surprising method of constructing curves with constant width: Draw as many straight lines as you like, but all mutually intersecting.

What Is A Differential Equation? A differential equation can look pretty intimidating, with lots of fancy math symbols. But the idea behind it is actually fairly simple: A differential equation states how a rate of change (a "differential") in one variable is related to other variables. For example, the single spring simulation has two variables: time t and the amount of stretch in the spring, x. If we set x = 0 to be the position of the block when the spring is unstretched, then x represents both the position of the block and the stretch in the spring. the rate of change in velocity is proportional to the position For instance, when the position is zero (ie. the spring is neither stretched nor compressed) then the velocity is not changing. On the other hand, when the position is large (ie. the string is very much stretched or compressed) then the rate of change of the velocity is large, because the spring is exerting a lot of force. What is a Solution to a Differential Equation? Initial Conditions

iFormazione: Costruire la matematica! Sicuramente una delle convinzioni maggiormente radicate in ogni matematico è che la matematica è bella, convinzione che sicuramente risulta estremamente misteriosa per chi matematico non è! Per cercare di spiegare la difficoltà di apprezzare la bellezza della matematica, spesso i matematici ricorrono al paragone con la musica. A nessuno, infatti, verrebbe in mente di dire che la musica è bella ascoltando un principiante che solfeggia o che si esercita nel suonare uno strumento, ripetendo magari per ore e ore sempre lo stesso pezzo. Dietro le immagini che avete già osservato c'è della matematica; la prima immagine rappresenta una bolla di sapone e quindi una superficie minima mentre la seconda riguarda un albero frattale; entrambe le immagini ad un primo impatto suscitano curiosità e bellezza. Costruite un quadrato 11x11 e suddividetelo così come mostrato nel primo quadrato in figura (potete costruire anche un quadrato 20x20 per un risultato più apprezzabile).

Acme's Wine Bottle Klein Bottle Acme's Wine Bottle Klein Bottle After 5 years of experimentation, I'm delighted to offer the Acme Klein Bottle Wine Bottle. Yes, you can store wine in it, and pour wine into and out of it. But no, it's not very practical as a wine carafe. The chimerical Wine Bottle Klein Bottle is now reality! The Wine Bottle Klein Bottle is difficult to fill with wine, because of vapor-lock. I've made the Wine Bottle Klein Bottle in two different shapes. Not only are these difficult to fill and empty, but cleaning them is a real challenge. I've designed these to balance with or without contents. Again, these are about the most impractical Wine Bottle / Caraffes ever made. photo below shows the short-handled variety: The short handled Wine Bottle Klein Bottle below: notice the handworked glass pouring spout! Go to Acme's Home Page, home to plenty of one-sided Klein Bottles

Geometry Geometry (from the Ancient Greek: γεωμετρία; geo- "earth", -metron "measurement") is a branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space. A mathematician who works in the field of geometry is called a geometer. Geometry arose independently in a number of early cultures as a body of practical knowledge concerning lengths, areas, and volumes, with elements of formal mathematical science emerging in the West as early as Thales (6th Century BC). By the 3rd century BC, geometry was put into an axiomatic form by Euclid, whose treatment—Euclidean geometry—set a standard for many centuries to follow.[1] Archimedes developed ingenious techniques for calculating areas and volumes, in many ways anticipating modern integral calculus. In Euclid's time, there was no clear distinction between physical and geometrical space. Overview[edit] Practical geometry[edit] Axiomatic geometry[edit] Geometry lessons in the 20th century

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