Pub Date : 1900-01-01DOI: 10.1017/S0950184300000306
W. L. Edge
{"title":"Miss C. M. Hamill","authors":"W. L. Edge","doi":"10.1017/S0950184300000306","DOIUrl":"https://doi.org/10.1017/S0950184300000306","url":null,"abstract":"","PeriodicalId":417997,"journal":{"name":"Edinburgh Mathematical Notes","volume":"462 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123976570","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1900-01-01DOI: 10.1017/S0950184300003074
W. Newns
A classical theorem of Cantor states that the class of all sub-classes of a given class has a cardinal greater than that of the given class. This theorem is here established in a sharpened form, which was suggested to me by a question set by Professor J. M. Whittaker, F.R.S, in the 1950 examination for the Honours B.Sc. Degree at Liverpool.
{"title":"A theorem on cardinal numbers","authors":"W. Newns","doi":"10.1017/S0950184300003074","DOIUrl":"https://doi.org/10.1017/S0950184300003074","url":null,"abstract":"A classical theorem of Cantor states that the class of all sub-classes of a given class has a cardinal greater than that of the given class. This theorem is here established in a sharpened form, which was suggested to me by a question set by Professor J. M. Whittaker, F.R.S, in the 1950 examination for the Honours B.Sc. Degree at Liverpool.","PeriodicalId":417997,"journal":{"name":"Edinburgh Mathematical Notes","volume":"119 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129208079","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1900-01-01DOI: 10.1017/S0950184300002615
W. Barrett
{"title":"A note on some networks of polygons","authors":"W. Barrett","doi":"10.1017/S0950184300002615","DOIUrl":"https://doi.org/10.1017/S0950184300002615","url":null,"abstract":"","PeriodicalId":417997,"journal":{"name":"Edinburgh Mathematical Notes","volume":"31 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130467838","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1900-01-01DOI: 10.1017/S0950184300000136
J. Wedderburn
The usual proofs of Desargues Theorem employ either metrical or analytical methods of projection from a point outside the plane; and if it is attempted to translate the analytical proof by the von Stuadt-Reye methods, the result is very long and there is trouble with coincidences. It is the object of this note to give a short geometrical proof which, in addition to the usual axioms of incidence and extension, uses only the assumption that a projectivity which leaves three points on a line unchanged also leaves all points on it unchanged. Degenerate cases are excluded as having no interest.
{"title":"On Desargues Theorem","authors":"J. Wedderburn","doi":"10.1017/S0950184300000136","DOIUrl":"https://doi.org/10.1017/S0950184300000136","url":null,"abstract":"The usual proofs of Desargues Theorem employ either metrical or analytical methods of projection from a point outside the plane; and if it is attempted to translate the analytical proof by the von Stuadt-Reye methods, the result is very long and there is trouble with coincidences. It is the object of this note to give a short geometrical proof which, in addition to the usual axioms of incidence and extension, uses only the assumption that a projectivity which leaves three points on a line unchanged also leaves all points on it unchanged. Degenerate cases are excluded as having no interest.","PeriodicalId":417997,"journal":{"name":"Edinburgh Mathematical Notes","volume":"4 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129543206","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1900-01-01DOI: 10.1017/S0950184300002664
H. W. Turnbull
Cardboard or wire models of ellipsoids and hyperboloids exist which consist of two sets of circular sections. They cover the quadric surface with curvilinear quadrilaterals, whose sides remain constant in length when the model alters in shape. In fact the models admit of one degree of freedom—they are collapsible—and the angle between the two sets of circular sections can be varied.
{"title":"Collapsible circular sections of quadric surfaces","authors":"H. W. Turnbull","doi":"10.1017/S0950184300002664","DOIUrl":"https://doi.org/10.1017/S0950184300002664","url":null,"abstract":"Cardboard or wire models of ellipsoids and hyperboloids exist which consist of two sets of circular sections. They cover the quadric surface with curvilinear quadrilaterals, whose sides remain constant in length when the model alters in shape. In fact the models admit of one degree of freedom—they are collapsible—and the angle between the two sets of circular sections can be varied.","PeriodicalId":417997,"journal":{"name":"Edinburgh Mathematical Notes","volume":"40 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129943746","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1900-01-01DOI: 10.1017/S095018430000286X
R. Goodstein
The object of this note is to outline a rigorous evaluation of Planck's integral by methods which presuppose no more than an elementary knowledge of the Calculus. The proof has been divided into four theorems each of which is of some interest in itself.
{"title":"On the evaluation of Planck's integral","authors":"R. Goodstein","doi":"10.1017/S095018430000286X","DOIUrl":"https://doi.org/10.1017/S095018430000286X","url":null,"abstract":"The object of this note is to outline a rigorous evaluation of Planck's integral by methods which presuppose no more than an elementary knowledge of the Calculus. The proof has been divided into four theorems each of which is of some interest in itself.","PeriodicalId":417997,"journal":{"name":"Edinburgh Mathematical Notes","volume":"29 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132125671","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1900-01-01DOI: 10.1017/S0950184300002585
R. Behari
1. It is known that (i) the line of striction of a ruled surface is the locus of points at which the geodesic curvatures of the orthogonal trajectories of the generators vanish, (ii) if at each point of a curve C on a surface, a tangent to the surface is drawn, and these tangents generate a ruled surface of which C is the line of striction, then, if each tangent is turned through a constant angle α about its point of contact in the tangent plane, the new set of tangents also form a ruled surface with C as a line of striction.
{"title":"Some properties of the line of striction of a ruled surface","authors":"R. Behari","doi":"10.1017/S0950184300002585","DOIUrl":"https://doi.org/10.1017/S0950184300002585","url":null,"abstract":"1. It is known that (i) the line of striction of a ruled surface is the locus of points at which the geodesic curvatures of the orthogonal trajectories of the generators vanish, (ii) if at each point of a curve C on a surface, a tangent to the surface is drawn, and these tangents generate a ruled surface of which C is the line of striction, then, if each tangent is turned through a constant angle α about its point of contact in the tangent plane, the new set of tangents also form a ruled surface with C as a line of striction.","PeriodicalId":417997,"journal":{"name":"Edinburgh Mathematical Notes","volume":"19 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134082767","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1900-01-01DOI: 10.1017/S0950184300000331
W. Mccrea
{"title":"W. M. H. Greaves","authors":"W. Mccrea","doi":"10.1017/S0950184300000331","DOIUrl":"https://doi.org/10.1017/S0950184300000331","url":null,"abstract":"","PeriodicalId":417997,"journal":{"name":"Edinburgh Mathematical Notes","volume":"9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133112675","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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