I denna uppsats presenteras grundläggande delar av hyperbolisk geometri. Uppsatsen är indelad i två kapitel. I första kapitlet studeras Möbiusavbildningar på Riemannsfären. Andra kapitlet presenterar modellen av hyperbolisk geometri i övre halvplanet H, skapad av Poincaré på 1880-talet.Huvudresultatet i uppsatsen är Gauss ? Bonnét´s sats för hyperboliska trianglar..

One of the purposes of this work was to find out what it means to have a conceptual understanding of geometry. It describes how the geometry evolved from history and the geometry that is taught in grade one to nine and collage. The area examined was based on fundamental geometric objects for example two- and three- dimensional objects and its characteristics and especially focusing on the areas of perimeter, area and volume. The literature- review showed that the conceptual understanding was primary to developing a good knowledge of geometry. The second purpose of his study examined whether pupils achieved the goals in geometry by working with a Mathematics Book.

The reason I am writing this essay is due to my curiosity on how children are interested in and how their understanding in geometry is at preschool years.My interest lies in children and arithmetic and especially geometry, which is something I belive that children deal with a great deal in their everyday routines, both in school and at home.What do children do when they work with geometry, and are they aware of what they do? To figure this out, I have taken my findings from three different interviews that I have done atmy preschool with a group of children that have been preselected.I am also curious about whether there is a difference in different types of schools. In this essay I have compared the preschool I work with a Montessori school and a third type of schoolwhere the children spends most of their day´s outdoors called ?Ur och Skur?In my results I can not see any major differences in these three preschools work with mathematics. The childrens knowledge is at a similar level and the work with geometry hasbeen implemented in a similar way..

The reason I am writing this essay is due to my curiosity on how children are interested in and how their understanding in geometry is at preschool years.My interest lies in children and arithmetic and especially geometry, which is something I belive that children deal with a great deal in their everyday routines, both in school and at home.What do children do when they work with geometry, and are they aware of what they do? To figure this out, I have taken my findings from three different interviews that I have done atmy preschool with a group of children that have been preselected.I am also curious about whether there is a difference in different types of schools. In this essay I have compared the preschool I work with a Montessori school and a third type of schoolwhere the children spends most of their day´s outdoors called ?Ur och Skur?In my results I can not see any major differences in these three preschools work with mathematics. The childrens knowledge is at a similar level and the work with geometry hasbeen implemented in a similar way..

This thesis is basically an attempt to discuss the intrinsic intersubjective nature of the so-called ideal sciences, i.e. geometry or arithmetic. Based upon a thorough analysis of Husserls The Origin of Geometry and Derridas Edmund Husserl's Origin of Geometry: an Introduction this thesis takes geometry as an example of an ideal science. The main question of the thesis is how an ideal science or object is constituted. The thesis consist of two main chapters - ?Geometry and Historicity? and ?Language?- and a concluding discussion.

Den här C-uppsatsen, som handlar om geometri, har tre ingående delar. Den första delen berättar geometrins historiska utveckling från de första Babyloniska skrifterna via kända matematiker som Pythagoras och Euklides fram till utvecklingen av den icke-euklidiska geometrin. Den andra delen förklarar mer ingående några hållpunkter som uppmärksammades ur geometrins historia. Denna del beskriver Euklides axiomatiska framställning och bevis av Pythagoras sats, konstruktion med passare och linjal, Apollonius kägelsnitt samt en inblick i grunderna för projektiv geometri. I den avslutande delen har en jämförande studie gjorts av fyra olika läromedel för gymnasieskolan.

Planet rendering plays an important role in universe visualization and geographic visualization. The recent tools and methods allow better data acquisition, usually with very high resolution. However in computer graphics, there is always the limitation on the resolution of geometry and texture due to numerical imprecision. Not many applications can handle high resolution data effectively.This thesis introduces, Implicit Surface Scene, a level of detail scene management inspired by dynamic coordinate system and SCALEGRAPH? which change over time depending on the current camera position relative to the planet surface.

Abstract CORDIC (Coordinate Rotation Digital Computer) is an iterative algorithm for the calculation of a two-dimensional vector in circular, linear or hyperbolic coordinate systems. This paper presents a survey of known CORDIC algorithms and architectures for the rotation and vectoring mode in the circular cordinate system. In addition an implementation of the differential CORDIC algorithm in VHDL has been done. The implementation is designed to keep the fast timing and throughput characteristic known for on-line redundant arithmetic..

This paper analyses the pricing on spare parts. Empirical studies have showed that manufacturers of durable goods make an unproportional large profit on its spare parts in relation to the revenue it generates. It is first showed that according to the standard economic model the price on spare part ought to be zero since the producer include an insurance in the price of the main good. Further it is showed that moral hazard alone do not explain the pricing found in the studies. Finally an analysis of whether consumers with present-biased preferences could be a possible explanation is made.

This master thesis work was done by two students at Machine Design at KTH for Lesjöfors Stockholmsfjäder AB. The task was to develop a calculation program for gas springs. The program is going to ease the selection of gas springs for a given case of a lid that should be opened. The program is going to be used internal by sales people at Lesjöfors AB in Sweden and internationally. The program is therefore written in English.The program was developed in Microsoft Visual C# 2008 Express Edition.

The thermal response of a borehole field is often described by non?dimensional response factors called gfunctions.The g?function was firstly generated as a numerical solution based on SBM (Superposition BoreholeModel). An analytical approach, the FLS (Finite Line Source), is also accepted for generating the g?function. In thiswork the potential to numerically produce g?functions is studied for circular borehole fields using the commercialsoftware COMSOL.

Skuggor är centrala för hur människan uppfattar världen. Inom datorspel och andra interaktiva 3D-applikationer är det viktigt att underlätta förståelsen av scenen och det finns även ofta en stark vilja att skapa realistiska miljöer. Detta samt att skuggsättning är en komplicerad och prestandakrävande operation gör det till ett viktigt område inom realtidsgrafik. Vi undersöker i denna avhandling relationen mellan prestandan (renderingstiden) för de två populära metoderna för skuggsättning inom realtidsgrafik, shadow mapping och shadow volumes. Undersökningen avgränsas till två utvalda varianter av de ursprungliga algoritmerna.

This paper gives an introduction to the theory of minimal surfaces. It is in- tended for undergraduate students with some basic knowledge of differential geometry and complex analysis.After defining the concept of minimal surface and giving a brief histo- rical survey, we look at some well-known minimal surfaces and a few of their characteristic properties. The connection between minimal surfaces and harmonic functions is discussed and the Weierstrass-Enneper represen- tation formulas are introduced. We also present Bjo?rling?s problem and give some examples. .

Skuggor är centrala för hur människan uppfattar världen. Inom datorspel och andra interaktiva 3D-applikationer är det viktigt att underlätta förståelsen av scenen och det finns även ofta en stark vilja att skapa realistiska miljöer. Detta samt att skuggsättning är en komplicerad och prestandakrävande operation gör det till ett viktigt område inom realtidsgrafik. Vi undersöker i denna avhandling relationen mellan prestandan (renderingstiden) för de två populära metoderna för skuggsättning inom realtidsgrafik, shadow mapping och shadow volumes. Undersökningen avgränsas till två utvalda varianter av de ursprungliga algoritmerna.

This paper gives an introduction to the theory of minimal surfaces. It is in- tended for undergraduate students with some basic knowledge of differential geometry and complex analysis.After defining the concept of minimal surface and giving a brief histo- rical survey, we look at some well-known minimal surfaces and a few of their characteristic properties. The connection between minimal surfaces and harmonic functions is discussed and the Weierstrass-Enneper represen- tation formulas are introduced. We also present Bjo?rling?s problem and give some examples. .