scholarly journals (1) An Introduction to Projective Geometry (2) Elementary Analysis (3) The School Algebra (Matriculation Edition) (4) A First Book in Algebra (5) A Second Book in Algebra (6) Plane and Solid Geometry (7) Plane Geometry: Practical and Theoretical, Pari Passu (8) Plane Geometry for Schools (9) Wightman's Secondary School Mathematical Tables

Nature ◽  
1922 ◽  
Vol 109 (2745) ◽  
pp. 737-739
Author(s):  
S. BRODETSKY
Keyword(s):  
Secondary School ◽  
Projective Geometry ◽  
Plane Geometry ◽  
Solid Geometry ◽  
Elementary Analysis

scholarly journals III. On abstract geometry

1870 ◽  
Vol 18 (114-122) ◽  
pp. 122-123
Keyword(s):  
General Theory ◽  
Linear Function ◽  
Rational Functions ◽  
Plane Geometry ◽  
System Of Equations ◽  
Fundamental Notion ◽  
Solid Geometry

I submit to the Society the present exposition of some of the elementary principles of an Abstract m -dimensional geometry. The science presents itself in two ways,—as a legitimate extension of the ordinary two- and threedimensional geometries; and as a need in these geometries and in analysis generally. In fact whenever we are concerned with quantities connected together in any manner, and which are, or are considered as variable or determinable, then the nature of the relation between the quantities is frequently rendered more intelligible by regarding them (if only two or three in number) as the coordinates of a point in a plane or in space; for more than three quantities there is, from the greater complexity of the case, the greater need of such a representation; but this can only be obtained by means of the notion of a space of the proper dimensionality; and to use such representation, we require the geometry of such space. An important instance in plane geometry has actually presented itself in the question of the determination of the curves which satisfy given conditions: the conditions imply relations between the coefficients in the equation of the curve; and for the better understanding of these relations it was expedient to consider the coefficients as the coordinates of a point in a space of the proper dimensionality. A fundamental notion in the general theory presents itself, slightly in plane geometry, but already very prominently in solid geometry; viz. we have here the difficulty as to the form of the equations of a curve in space, or (to speak more accurately) as to the expression by means of equations of the twofold relation between the coordinates of a point of such curve. The notion in question is that of a k -fold relation,—as distinguished from any system of equations (or onefold relations) serving for the expression of it,—and giving rise to the problem how to express such relation by means of a system of equations (or onefold relations). Applying to the case of solid geometry my conclusion in the general theory, it may be mentioned that I regard the twofold relation of a curve in space as being completely and precisely expressed by means of a system of equations (P = 0, Q = 0, . . T = 0), when no one of the func ions P, Q, ... T, as a linear function, with constant or variable integral coefficients, of the others of them, and when every surface whatever which passes through the curve has its equation expressible in the form U = AP + BQ ... + KT., with constant or variable integral coefficients, A, B ... K. It is hardly necessary to remark that all the functions and coefficients are taken to be rational functions of the coordinates, and that the word integral has reference to the coordinates.

An Easy Proof for Some Classical Theorems in Plane Geometry

1992 ◽  
Vol 35 (4) ◽  
pp. 560-568 ◽  
Author(s):  
C. Thas
Keyword(s):  
Projective Plane ◽  
Projective Geometry ◽  
The Other ◽  
Plane Geometry ◽  
The Real ◽  
Easy Proof ◽  
Special Cases ◽  
Euclidean Planes ◽  
Straight Lines ◽  
Short Method

AbstractThe main result of this paper is a theorem about three conies in the complex or the real complexified projective plane. Is this theorem new? We have never seen it anywhere before. But since the golden age of projective geometry so much has been published about conies that it is unlikely that no one noticed this result. On the other hand, why does it not appear in the literature? Anyway, it seems interesting to "repeat" this property, because several theorems in connection with straight lines and (or) conies in projective, affine or euclidean planes are in fact special cases of this theorem. We give a few classical examples: the theorems of Pappus-Pascal, Desargues, Pascal (or its converse), the Brocard points, the point of Miquel. Finally, we have never seen in the literature a proof of these theorems using the same short method see the proof of the main theorem).

A Maintenance Program for Tenth Grade Mathematics

1932 ◽  
Vol 25 (4) ◽  
pp. 204-208
Author(s):  
C. C. Pruitt
Keyword(s):  
High School ◽  
School Curriculum ◽  
Senior High School ◽  
Plane Geometry ◽  
High School Curriculum ◽  
Solid Geometry ◽  
Maintenance Program ◽  
Tenth Grade

Probably no subject in the high school curriculum is receiving more attention today than that of plane geometry in the tenth grade. Much of this attention is directed towards the possibility of fusing plane and solid geometry into one course. From this situaation, one would infer that all is not well in either the field of plane geometry or that of solid, with probability in both. I think all teachers of mathematics in the senior high school are agreed that the teaching of plane geometry has not advanced to the point where we are satisfied with the results obtained.

The 17th Annual Meeting of the National Council of Teachers of Mathematics

1936 ◽  
Vol 29 (4) ◽  
pp. 186-192
Author(s):  
Edwin W. Schreiber
Keyword(s):  
High School ◽  
New York ◽  
Secondary School ◽  
Annual Meeting ◽  
American Mathematical Society ◽  
School Mathematics ◽  
Annual Business ◽  
National Council ◽  
Mathematical Association ◽  
Solid Geometry

The Seventeenth Annual Meeting ofthe National Council of Teachers of Mathematics was held in St. Louis, Missouri, December 31, 1935 to January 1, 1936. This is the first annual meeting the National Council has held with the A.A.A.S. One hundred eighty-four registered for the meetings though the total attendance was well in excess of two hundred. A joint session with Section A of the A.A.A.S., the American Mathematical Society, and the Mathematical Association of America, was held on Tuesday morning, December 31, with approximately 250 in attendance. Professor Kenncth P. Williams of I ndiana University presented a temporary report of the Joint Commission on the Place of Mathematics in the Secondary School. “The Main Purposes and Objectives in Teaching High School Mathematics” was discussed by William Betz of Rochester, New York, representing the National Council, and W. W. Hart, representing the Mathematical Association of America. On Tuesday afternoon the National Council presented a Symposium on the Teaching of Geomcetry. Professor W. H. Roever of Washington University, St. Louis, discussed in a very thorough manner the 11Purpose, Nature, and use of Pictures in the Teaching of Solid Geometry.” John T. Rule, the Taylor School, Clayton, Missouri, presented an interesting paper on “Stereoscopy as an Aid to the Teaching of Solid Geometry.” The session closed with a stimulating discussion by Rolland R. Smith, Classical High School, Springfield, Mass., on “Developing the Meaning of Demonstration in Geometry.” The Tuesday evening session was opened by an address of welcome by the Rev. Father Robert S. Johnston, President of St. Louis University. The response was made by Miss Edith Woolsey of Minneapolis, Minnesota. Professor Edwin W. Schreiber, State Teachers College, Macomb, Illinois, presented an illustrated lecture on “The History of the Development of the Metric System.” Miss Ruth Lane, University High School, Iowa City, Iowa, presented an illuminating paper on “Mathematical Recreations, an Aid or a Relief?” On Wednesday morning, J anuary 1, the Annual Business session of the National Council was held. At this session Professor H. E. Slaught of the University of Chicago was honored in being elected Honorary President of the National Council. Secretary Schreiber as Chairman of the Ballot Committee announced the results of the annual election: President—Miss Martha Hildebrandt, Proviso Township High School, Maywood, Illinois; second Vice President-Miss Mary Kelly, Wichita, Kansas; three new members of the Board of Directors—E. R. Breslich, Chicago, Illinois, Leonard D. Haertter, Clayton, Missouri, and Virgil S. Mallory, Montclair, New Jersey. The morning session closed with two interesting papers: “Functiona! Thinking and Teaching in Secondary School Mathematics” by Professor H. C. Christofferson, Miami University, Oxford, Ohio; and “The Crisis in Mathematics—at Rome and Abroad— by Professor William D. Reeve, Teachers

An Achievement test in Solid Geometry

1928 ◽  
Vol 21 (3) ◽  
pp. 151-162
Author(s):  
Louis A. McCoy
Keyword(s):  
Secondary School ◽  
Subject Matter ◽  
Achievement Test ◽  
School Mathematics ◽  
The Other ◽  
Good Teacher ◽  
Secondary School Mathematics ◽  
Solid Geometry ◽  
The Subject ◽  
The Right

In the work of teaching secondary school mathematics in a large school where there are as many as twelve different divisions of the same subject, it would be very interesting and indeed very enlightening to see the different grades of work being done. Different teachers have their own pet ways of doing things, of presenting new matter, of conducting recitations, of drilling on old matter, of developing mathematical power in their pupils, etc. And yet they are all striving for the same results. The fact that one teacher's pupils consistently attain better results naturally should put a premium on that teacher's methods, and the work of the department would be improved if some of the other teachers would take a leaf out of the successful teacher's book. Students will often remark “So and So is a good teacher; I get a lot out of his class; he makes things clear; he has good discipline; he certainly gets the stuff over, etc.”An inspector visits the class, notes the attitude of the pupils, the personality and skill of the teacher, and oftentimes is familiar enough with the subject matter of the recitation to see if the pupils are catching and giving back the right things, and then grades the teacher as an Al man, for example. But does the opinion of the boys themselves or the visitor answer the question whether or not the teacher is successful in giving his subject to the pupils? Don't we need something more objective, more tangible, more exact on which to pin our faith? In general the supervisors are hitting it right, also the students, but we think we can do better.

Viewing the World from Different Angles: Plato’s Timaeus 54E-55A

Apeiron ◽  
2013 ◽  
Vol 46 (3) ◽  
pp. 244-269
Author(s):  
Ernesto Paparazzo
Keyword(s):  
Present Article ◽  
Solid Angle ◽  
Alternative Interpretation ◽  
Plane Geometry ◽  
A Value ◽  
Solid Geometry ◽  
The World ◽  
Euclid’S Elements ◽  
Solid Angles ◽  
The Universe

Abstract The present article investigates a passage of the Timaeus in which Plato describes the construction of the pyramid. Scholars traditionally interpreted it as involving that the solid angle at the vertex of the pyramid is equal, or nearly so, to 180°, a value which they took to be that of the most obtuse of plane angles. I argue that this interpretation is not warranted, because it conflicts with both the geometrical principles which Plato in all probability knew and the context of the Timaeus. As well as recalling the definitions and properties of plane angles and solid angles in Euclid’s Elements, I offer an alternative interpretation, which in my opinion improves the comprehension of the passage, and makes it consistent with both the immediate and wider context of the Timaeus. I suggest that the passage marks a transition from plane geometry to solid geometry within Plato’s account of the universe.

Descriptive geometry in middle school mathematics teaching in Japan (1905-1946)

2020 ◽  
pp. 57-72
Author(s):  
Kei Kataoka
Keyword(s):  
Middle School ◽  
Secondary School ◽  
20Th Century ◽  
School Curriculum ◽  
Descriptive Geometry ◽  
Early 20Th Century ◽  
Meiji Restoration ◽  
Solid Geometry ◽  
Secondary School Curriculum ◽  
And Mathematics

Teaching of descriptive geometry began in 18th-century France and became widespread in tertiary and secondary education worldwide throughout the 19th century. Until the 20th century, educators often described two aims of descriptive geometry – technical education and mathematics education. In Japan, descriptive geometry was introduced into engineering and artistic higher education after the Meiji Restoration of 1868. Descriptive geometry became part of the general secondary school curriculum in the 1880s, but it had been taught under the auspices of arts and crafts education rather than mathematics. In the early 20th century, Japanese mathematics educators began to focus on descriptive geometry as a way to reform solid geometry. When Japan’s secondary school curriculum was revised in 1942, descriptive geometry was included in solid geometry and mathematics for the first time. Although this curriculum lasted only until 1946, it was the fruit of many educators’ labors and is worthy of examination. This paper examines several books and documents from the early 20th-century Japan and shows that there was a technical, mathematics-oriented debate about the aim of descriptive geometry teaching as seen in Europe. Keywords: descriptive geometry, solid geometry, secondary school, middle school, Nobutaro Nabeshima, Minoru Kuroda

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