Geometrography with applications to the instruments of the draftsman
| dc.contributor.advisor | Not available | |
| dc.creator | Newton, Guy Thornwel | |
| dc.date.accessioned | 2019-03-26T21:21:57Z | |
| dc.date.available | 2019-03-26T21:21:57Z | |
| dc.date.issued | 1926 | |
| dc.description | The purpose of this thesis is to devise elementary constructions which are the bases of all construction; first, with compasses alone; second, with compasses plus the ruler; third, with compasses and ruler plus the triangles. Along with these constructions a system of Geometrography will be used to measure each construction and a comparison will be made of the three methods used. The central idea is to investigate and ascertain whether a number of the elementary constructions given in our Plane Geometries can be made practically as short and in some cases shorter by use of the compasses alone; and further to see how much shorter they can be made by introducing the triangles in Plane Geometry. Suppose we have a construction problem which can be solved by compasses alone and also with ruler and compasses; and further, suppose 'compasses-alone' construction is somewhat longer than the ruler and compasses construction. Which method is more desirable for accuracy? When a line is drawn by the aid of a straight edge, it may be in error for three reasons: first, the straight edge may not coincide with the point or points through which the line is to be drawn; second, the straight edge is likely to be moved as the line is being ruled; and third, the angle of elevation of the pen may not remain constant as the line is being ruled. When points are located by use of the compasses, they may be in error for only one reason: the operation of making the points of the compasses coincide with the reference points. However, this error is not so likely with points of the compasses as with ruler. There is no chance of error from the points of the compasses being moved as the circle is drawn for one leg of the compasses is anchored in the paper. Further, there is no chance of error from the angle of elevation of the compasses with the plane of the paper not being constant. Thus from the point of view of accuracy a 'compass-alone' construction is more desirable than a ruler and compasses construction, even though the 'compasses-alone' construction is longer. The errors that may occur by use of the triangles are the same as those occurring by the use of the ruler. | |
| dc.description.department | Mathematics | en_US |
| dc.format.medium | electronic | en_US |
| dc.identifier.uri | https://hdl.handle.net/2152/73743 | |
| dc.identifier.uri | http://dx.doi.org/10.26153/tsw/876 | |
| dc.language.iso | eng | en_US |
| dc.relation.ispartof | UT Electronic Theses and Dissertations | en_US |
| dc.rights | Copyright © is held by the author. Presentation of this material on the Libraries' web site by University Libraries, The University of Texas at Austin was made possible under a limited license grant from the author who has retained all copyrights in the works. | en_US |
| dc.rights.restriction | Open | en_US |
| dc.subject.lcsh | Geometrical constructions | |
| dc.subject.lcsh | Mechanical drawing--Mathematics | |
| dc.subject.lcsh | Mechanical drawing--Instruments | |
| dc.title | Geometrography with applications to the instruments of the draftsman | en_US |
| dc.type | Thesis | en_US |
| dc.type.genre | Thesis | en_US |
| thesis.degree.department | Mathematics | en_US |
| thesis.degree.discipline | Mathematics | en_US |
| thesis.degree.grantor | University of Texas at Austin | en_US |
| thesis.degree.level | Masters | en_US |
| thesis.degree.name | Master of Arts | en_US |