Pub Date : 1900-01-01DOI: 10.1017/S0950184300000215
A. G. Walker
In this article is described the construction of a thread model of a hyperboloid of one sheet ( H ) and its asymptotic cone ( C ). It ia simple to make, requiring only cardboard and thread, and can be made collapsible and of pocket size if desired. The model consists of two hinged pieces of cardboard (intersecting planes π and ) on which are drawn circles S H , respectively in which the planes meet H , and the concentric circles S C , respectively in which the planes meet C . A number of generators of the same system on H are now represented by threads joining S H and , and the corresponding parallel generators of C are represented by threads joining S C and . In order to ensure that these generators are well spaced, those of C are taken at equal eccentric angles apart in a principal elliptic section. The main theorem used in the design is that if l a generator of C , then the tangent plane to C at points of l meets H in two generators both of which are parallel to l
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Pub Date : 1900-01-01DOI: 10.1017/S0950184300000100
N. Walls
Morley's theorem states that if ABC be any triangle, and if those trisectors of the angles B and C adjacent to BC meet in L , and M , N be similarly constructed, then the triangle LMN is equilateral.
{"title":"An Elementary Proof of Morley's Trisector Theorem","authors":"N. Walls","doi":"10.1017/S0950184300000100","DOIUrl":"https://doi.org/10.1017/S0950184300000100","url":null,"abstract":"Morley's theorem states that if ABC be any triangle, and if those trisectors of the angles B and C adjacent to BC meet in L , and M , N be similarly constructed, then the triangle LMN is equilateral.","PeriodicalId":417997,"journal":{"name":"Edinburgh Mathematical Notes","volume":"197 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":"116147854","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/S0950184300000070
A. Aitken
{"title":"On the Number of Distinct Terms in the Expansion of Symmetric and Skew Determinants","authors":"A. Aitken","doi":"10.1017/S0950184300000070","DOIUrl":"https://doi.org/10.1017/S0950184300000070","url":null,"abstract":"","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":"116671965","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/S0950184300000112
A. Waterson
{"title":"An Expansion for x n + y n","authors":"A. Waterson","doi":"10.1017/S0950184300000112","DOIUrl":"https://doi.org/10.1017/S0950184300000112","url":null,"abstract":"","PeriodicalId":417997,"journal":{"name":"Edinburgh Mathematical Notes","volume":"37 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":"114134441","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/S0950184300003098
G. Stokes
The apparatus consists of a base piece with central line X'OX •carrying on OX a uniform scale suitably graduated. An upright piece OY is fixed rigidly at right angles to the base piece and carries a scale marked " y " at R, where OR = /y. An arm PQ, made of transparent material, can rotate about the pivot P, which is attached to a slide moveable along X'O, and carries a uniform scale whose unit is half that of the OX scale.
{"title":"Mechanical devices for solving quadratic and cubic equations","authors":"G. Stokes","doi":"10.1017/S0950184300003098","DOIUrl":"https://doi.org/10.1017/S0950184300003098","url":null,"abstract":"The apparatus consists of a base piece with central line X'OX •carrying on OX a uniform scale suitably graduated. An upright piece OY is fixed rigidly at right angles to the base piece and carries a scale marked \" y \" at R, where OR = /y. An arm PQ, made of transparent material, can rotate about the pivot P, which is attached to a slide moveable along X'O, and carries a uniform scale whose unit is half that of the OX scale.","PeriodicalId":417997,"journal":{"name":"Edinburgh Mathematical Notes","volume":"30 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":"127554751","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/S0950184300002913
A. Macintyre
{"title":"Euler's limit for e x and the exponential series","authors":"A. Macintyre","doi":"10.1017/S0950184300002913","DOIUrl":"https://doi.org/10.1017/S0950184300002913","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":"133122102","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/S0950184300000203
AGNES H. Waddell
In many cases, when a colony of micro-organisms such as moulds, yeasts or bacteria grows on the plane surface of a solid medium ( e.g. agar), starting from a single cell, the colony tends to grow as an ever expanding circle. The reason for this is that every cell, if free from competition, can multiply at roughly a constant rate in all directions in a plane, limited by the fact that territory occupied by one cell cannot be occupied by another. For the purposes of the present discussion, we can assume, as a first approximation, that the whole process is two-dimensional.
{"title":"Curves formed by colonies of micro-organisms growing on a plane surface","authors":"AGNES H. Waddell","doi":"10.1017/S0950184300000203","DOIUrl":"https://doi.org/10.1017/S0950184300000203","url":null,"abstract":"In many cases, when a colony of micro-organisms such as moulds, yeasts or bacteria grows on the plane surface of a solid medium ( e.g. agar), starting from a single cell, the colony tends to grow as an ever expanding circle. The reason for this is that every cell, if free from competition, can multiply at roughly a constant rate in all directions in a plane, limited by the fact that territory occupied by one cell cannot be occupied by another. For the purposes of the present discussion, we can assume, as a first approximation, that the whole process is two-dimensional.","PeriodicalId":417997,"journal":{"name":"Edinburgh Mathematical Notes","volume":"38 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":"130592485","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/S0950184300002834
N. Walls
where Ar is the r' A complete homogeneous symmetric function in a set of n arguments, is equal to the quotient of a particular pair of alternants was shown essentially by Jacobi in 1841 and by Trudi in 1864. The present note exhibits this well-known relation, (3), as the immediate consequence of a simple matrix equality. The symmetric functions hr are connected with the elementary symmetric functions ar in the same n arguments a, /?, . . . , K by the Wronski relations Og/tj — axh0 = 0, a0h2 — a1h1 + ath0 = 0, aohs — ajiz + «2^i — 3^o = 0>
{"title":"A note on an identity of Jacobi's","authors":"N. Walls","doi":"10.1017/S0950184300002834","DOIUrl":"https://doi.org/10.1017/S0950184300002834","url":null,"abstract":"where Ar is the r' A complete homogeneous symmetric function in a set of n arguments, is equal to the quotient of a particular pair of alternants was shown essentially by Jacobi in 1841 and by Trudi in 1864. The present note exhibits this well-known relation, (3), as the immediate consequence of a simple matrix equality. The symmetric functions hr are connected with the elementary symmetric functions ar in the same n arguments a, /?, . . . , K by the Wronski relations Og/tj — axh0 = 0, a0h2 — a1h1 + ath0 = 0, aohs — ajiz + «2^i — 3^o = 0>","PeriodicalId":417997,"journal":{"name":"Edinburgh Mathematical Notes","volume":"107 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":"133459067","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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