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. .

Visual Type Instrument - VTI, is a tool containing a typeface and a set of geometric calculations that generates numerical data in spreadsheets. The data is determined from the typefaces visual dimensions and is used to calculate leading, type size, margins and format. The aim is to offer, for all of those working with typography and design, a practical way to manage text, image and format in relationship to visual size. Instead of using point measurements, VTI uses a new device called Edo. An Edo is the same as one twelfth of a millimetre.

This thesis work has been performed at Volvo Aero Corporation in Trollhättan, at the department of ?hot structures? involving aircraft engine GP7000. The purpose with the study was to investigate the possibility to reduce size of the forging of flanges on the rear turbine frame when purchasing. Thereto examine the parameters that affect the flanges motion during the manufacturing process. The goal was to provide Volvo Aero with foundation to later bring in slimmed forgings.

The borehole heat exchangers of today suffer from poor thermal and hydrodynamic performance. The purpose of this thesis is to improve the performance of ground source heat pump systems and thermal energy storages by increasing the energy efficiency of the borehole heat exchangers. For this reason, the annular coaxial borehole heat exchanger (CBHE) has been analyzed. This type of heat exchanger is interesting in terms of both thermal and hydrodynamic performance. A model has been set up in the program Comsol Multiphysics in order to investigate the heat transfer characteristics along the borehole.

The purpose of this master thesis has been to find different solutions to the design of a headlamp with a cluster of three or possibly four high power LEDs (Light Emitting Diodes). During the work, two different problems have been considered; how to design a lens in order to shape the light beam in a desirable way, and how to design a cooling system which will lower the temperature of the LEDs as efficiently as possible, still taking into account the Geometry set by the optical solution as well as other given geometries. The results presented in this thesis are partly the outcome of a literature study, but derive mainly from a number of tests and measurements made on two test rigs and one concept prototype..

This is a thesis written for a master's degree at the Computer Vision Laboratory, University of Linköping. An abstract outer product is defined and used as a bridge to reach 2:nd and 4:th order tensors. Some applications of these in geometric analysis of range data are discussed and illustrated. In idealized setups, simple geometric objects, like spheres or polygons, are successfully detected. Finally, the generalization to n:th order tensors for storing and analysing geometric information is discussed..

Tractors of today come equipped with a CAN-system. A CAN-system sends information from sensors to electronic control units who process the signals. The sensors measure several interesting parameters such as force, pressure and speed for various components of the tractor. This thesis discuss a force sensor which is placed in the pivot of the tractors three point linkage, the sensor measure the horizontal reaction force from the load that the tractor is exposed to. Signals from this sensor can be used to measure the force from any implement that the tractor is exposed to during an operation.

The purpose of this study is to observe which method that is used when it comes to teaching Geometry. The study aims to take a closer look at four different ways of teaching: illustrations, using practical objects, brainstorming and verbal communication. The method used to get the results is observation. With the result, we can deduce primarily that the educators make use of the four didactic methods to varying degrees. There are similarities between most of the teachers but also differences between them.

I denna uppsats studeras förekomsten av värden i geometrikapitel i läromedel för gymnasieskolans Matematik A. En metod baserad på innehållsanalys som använts i en tidigare studie om förekomst av värden i algebrakapitel har vidareutvecklats. Sammanlagt 955 uppgifter i geometrikapitlen i fem olika läroböcker har analyserats. Resultatet visar på en skillnad mellan intentionerna i gymnasieskolans styrdokument och det utrymme olika värden ges. Även skillnader mellan det utrymme studerade läromedel ger åt olika värden har påvisats..

LEDAthe chair as representativean exploring work on added value throughaesthetics and function.The project deals with portraying a chair. A chair thatwill raise questions regarding added value, questioning oursurroundings and not taking things for granted. Through anumber of properly selected words, I have built a collectionof objects that possess the basis of a chair. The words arebased on sources of inspiration; I picked up over the yearsand can be seen as a part of me and my inner self. QuestionsI asked myself concerns the impact of aesthetic and how itrelates to the function.

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..

Vi började vårt projekt med grunderna till verktyg för att utveckla spel i 2d. Dessa ämnade vi färdigställa under projektet och med dem utveckla en speldemo. Eftersom vi hade gemensamma visioner om spelutveckling så bestämde vi oss för att samarbeta, och fokusera på våra respektive områden. Med att utveckla egna verktyg ville vi få en större förståelse för de grundläggande mekanismerna av en spelmotor och möjligheten att påverka dessa efter våra specifika behov. Det var också för att hålla koden fri från licensierade komponenter för att i framtiden kunna underlätta distribution..

Syftet med den här rapporten är att se om elever som har svårigheter inom ett specifikt matematiskt område får den undervisning de behöver för att nå upp till målen. En diagnos gjordes med elever i år fyra inom området geometri. De har därefter haft en lektion där en pedagog blivit filmad. Därefter gjordes ytterligare en diagnos med eleverna för att se om resultatet är bättre, sämre eller är oförändrat. Det insamlade materialet analyserades ur ett variationsteoretiskt perspektiv.

This essay concerns the interpretation of house plans in three-aisled longhouses and hall-buildings, in Scandinavia during Iron Age. Full scale house reconstructions need a better basis of interpretations to understand the patterns of roof supporting post holes in excavated house plans. This has led to the thesis, presented here, that the layout of house plans during Iron Age is based on geometrical proportions. In order to prove this, geometric house plans were applied and compared with excavated house plans in 11different case studies, including the fortification of Fyrkat Denmark. It was found that all house plans in the case studies indicate, that the geometrical proportions 1:2, 1:3 and 2:3 of a given circle must have been used for the basic layout of the roof supporting post holes, using a compass and a straightedge.

Ett flertal både internationella och nationella undersökningar visar att svenska skolelever blir allt sämre på matematik. Ett delområde som ofta utpekas är geometri. Denna undersökning syftar till att ta reda på hur ämnet geometri har utvecklats i den svenska skolan samt vilka metoder och begrepp lärare använder sig av när de undervisar i geometri i de tidigare skolåren. Empirin har hämtats från åtta semistrukturerade intervjuer och från studier av gamla läroplaner. Resultatet visar att lärare använder en mängd begrepp och metoder i sin undervisning men att det finns ett behov av fortbildning hos lärarna.