This is sometimes called the Euler circle but this incorrectly attributes the result.
Dette er undertiden kaldes Euler cirkel men dette forkert attributter resultatet.
Other geometric investigations led him to fundamental ideas in topology such as the Euler characteristic of a polyhedron.
Andre geometriske undersøgelser førte ham til de grundlæggende idéer i topologi såsom Euler karakteristisk for et polyhedron.
He also worked on the Euler- Maclaurin summation formula.
Han arbejdede også på Euler- Maclaurin summering formel.
The Euler characteristic of the sphere is 2 so the integral of the curvature of 4π is 2π2.
Det Euler karakteristisk for området er 2 så integreret i krumningen af 4π 2π2.
The value of two is said to be the Euler characteristic of each of the polyhedra.
Den vaerdi af to, siges at være den Euler karakteristisk for hver af de polyhedra.
Thus the Euler characteristic is 2 for a regular polyhedron but 0 for a torus-like polyhedron.
Således den Euler kendetegn er 2 for en regelmæssig polyhedron men 0 for en torus-gerne polyhedron.
Description The gamma function returns the result of the Euler gamma function of z, commonly written as Γ z.
Beskrivelse Funktionen gamma returnerer resultatet af Eulers gammafunktion for z, almindeligvis skrevet som Γ z.
This means that the Euler characteristic is a topological invariant because it is not altered by any continuous mapping.
Det betyder, at den Euler kendetegn er en TOPOLOGISKE invariant fordi det ikke aendres ved en kontinuerlig kortlaegning.
The topics discussed are: the Jordan curve theorem,the map colouring problem, the Euler characteristic and the classification of surfaces.
De emner, der drøftes, er: Jordan kurve sætning,kortet farve problemet, Euler karakteristisk og klassificering af overflader.
The Euler characteristic of a torus(doughnut) is zero so the integral of the curvature over the torus is also zero.
Det Euler karakteristik af en torus(ringformet) er nul for integralet for krumning over torus er også nul.
Later he worked in celestial mechanics producing new methods of calculating orbits from three observations based on solving the Euler- Lambert equations.
Senere arbejdede han i himmelsk mekanikere at producere nye metoder til beregning af kredsløb fra tre observationer baseret på løse Euler- Lambert ligninger.
Returns the value of the Euler beta function evaluated for the arguments.
Beta-funktion Returnerer værdien af Eulers betafunktion evalueret for argumenterne.
Other work of Ostrowski was on the Cauchy functional equation, the Fourier integral formula,Cauchy-Frullani integrals, and the Euler- Maclaurin formula.
Andet arbejde Ostrowski var på Cauchy funktionelle ligning, Fourier integreret formel,Cauchy-Frullani integrals, og Euler- Maclaurin formel.
Thus the Euler formula is verified for prisms.The reason for choosing to work with prisms is that it is simple to deal with holes for them.
Den Euler formel kontrolleres for Prismer. Begrundelse for valg til at arbejde med Prismer er, at det er let at håndtere huller for dem.
Probably Hecke's most important work was in 1936 with his discovery of the properties of the algebra of Hecke operators and of the Euler products associated with them.
Sandsynligvis Hecke's vigtigste arbejde var i 1936 med sin opdagelse af egenskaberne for algebra af Hecke operatører og af Euler produkter forbundet med dem.
He considered the Euler angles and studied rotational problems which were motivated by the problem of the precession of the equinoxes.
Han behandlede Euler vinkler og studeret roterende problemer, der var motiveret af problemet med de præcession af equinoxes.
Euler also studied other unproved results of Fermat andin so doing introduced the Euler phi function(n), the number of integers k with 1 k n and k coprime to n.
Euler også studeret andre unproved resultaterne af Fermat ogdermed introducerede Euler phi funktion(n), antallet af heltal k med 1 k n og k Indbyrdes primisk til n.
This is sometimes called the Euler circle but this incorrectly attributes the result. Feuerbach also proved that the nine point circle touches the inscribed and three escribed circles of the triangle.
Dette er undertiden kaldes Euler cirkel men dette forkert attributter resultatet. Feuerbach også bevist, at de ni point cirkel berører afmærkes og tre escribed kredse af trekanten.
It is also shown that this procedure can be applied to a class of two point boundary value problems containing the Euler- Lagrange equation for simple variational problems and most second order ordinary differential equations.
Det er også vist, at denne fremgangsmåde kan anvendes på en klasse med to point grænse værdi problemer indeholdende Euler- Lagrange ligning for simple variational problemer og de fleste anden orden ordinære differentialligninger.
The thesis contains a different proof of the fact just shown by Lefschetz that for any closed manifold the sum of the indices of a generic vector field is a topological invariant,namely the Euler characteristic.
Afhandlingen indeholder et andet bevis på, netop vist ved Lefschetz, at der for enhver lukket manifold summen af indekser for en generisk vektor felt er en topologisk invariant,nemlig Euler karakteristik.
My own interest in the integrals of the Euler- Laplace type dates, I think, from the time when Sir Edmund Whittaker gave some properties of the Laplace transformation in his lectures at Cambridge in 1903 or 1904.
Min egen interesse i integrals af Euler- Laplace type datoer, tror jeg, fra det tidspunkt, hvor Sir Edmund Whittaker gav nogle egenskaber ved Laplace transformation i hans forelæsninger på Cambridge i 1903 eller 1904.
If such extrusions were extended from the top and bottom andbent to meet the effect on the Euler characteristic would be the same as in the creation of a hole in the prism; i.e.
Hvis sådanne Strengpressede blev forlænget fra den øverste og nederste ogBoejede at opfylde den indvirkning paa den Euler karakteristiske ville være den samme som i oprettelsen af et hul i PRISM; dvs.
The change in the Euler characteristic for a prism with a pit is therefore ΔΧ 2N- 4N+ 2N 0 The same construction could be carried out from the bottom face and the same results in terms of faces, edges and vertices would prevail.
Ændringen i det Euler KARAKTERISTISK FOR EN PRISM med en sten er derfor ΔΧ 2N- 4N+ 2N 0 Samme konstruktion vil kunne gennemfoeres fra bunden ansigt og de samme resultater med hensyn til flader, kanter og tabel er fremherskende.
Note that the right-hand side of the formula fits into the scheme of the Gauss-Bonnet Theorem in that the Euler characteristic of a plane polygon is just 1 because for a polygon there is 1 face and the number of edges and vertices are equal.
Bemærk, at højre side af formlen passer ind i ordningen af Gauss-Bonnet Theorem i, at Euler karakteristik af en planet polygon er kun 1 fordi en polygon er der 1 face og antallet af kanter og knudepunkter er ens.
He published a number of major pieces of work through the 1750s setting up the main formulae for the topic, the continuity equation,the Laplace velocity potential equation, and the Euler equations for the motion of an inviscid incompressible fluid.
Han har offentliggjort en række store stykker af arbejdet gennem 1750'erne om oprettelse af de vigtigste formler for det emne, kontinuitet ligning,Laplace hastigheds potentiale ligningen, og Euler ligninger for forslaget om en inviscid incompressible flydende.
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