Elements of Analytical Geometry. Vol. I. Straight Line and Circle

1932 ◽  
Vol 16 (217) ◽  
pp. 51
Author(s):  
N. M. Gibbins ◽  
J. I. Craig
Keyword(s):  
Analytical Geometry ◽  
Straight Line

1405. A Note on the Analytical Geometry of the Straight Line

1939 ◽  
Vol 23 (256) ◽  
pp. 387
Author(s):  
F. H. V. Gulasekharam
Keyword(s):  
Analytical Geometry ◽  
Straight Line

Analytical Geometry of the Straight Line

1933 ◽  
Vol 17 (226) ◽  
pp. 344
Author(s):  
N. M. Gibbins ◽  
W. M. Baker
Keyword(s):  
Analytical Geometry ◽  
Straight Line

Curves with corners

1962 ◽  
Vol 55 (5) ◽  
pp. 326-329
Author(s):  
Clarence R. Perisho
Keyword(s):  
Step Function ◽  
Analytical Geometry ◽  
Line Segments ◽  
Absolute Value ◽  
Geometric Figures ◽  
Straight Line ◽  
The Absolute ◽  
Continuous Curves ◽  
Sharp Corners

The graphs of functions usually studied in algebra and analytical geometry are smooth, continuous curves, with no sharp corners or discontinuities. There is, however, a certain fascination about equations that represent curves with unusual characteristics. The absolute-value notation can be used to write equations for many common geometric figures1 and to simplify equations which involve the step function.2 Absolute-value notation can also be used to write the equations of graphs involving straight-line segments with any number of corners or vertices.

On the Curriculum of Mathematics

1910 ◽  
Vol 3 (1) ◽  
pp. 1-8
Author(s):  
Eugene R. Smith ◽  
Jonathan T. Rorer ◽  
Isaac J. Schwatt
Keyword(s):  
Secondary Mathematics ◽  
Mathematical Concept ◽  
The Other ◽  
Clear Understanding ◽  
Satisfactory Explanation ◽  
Analytical Geometry ◽  
Straight Line ◽  
True Meaning ◽  
Long Time ◽  
Similar Triangles

The student must thoroughly understand the meaning and the philosophy, so to speak, of each mathematical concept presented to him. It takes a long time before he familiarizes himself so thoroughly with the conceptions of any mathematical subject so that he gets their significance, meaning and spirit, and the ability and facility to apply them readily. Few students have a clear understanding of the quantitative meaning and significance of the theorems of proportion, such as: “A line drawn parallel to a side of a triangle divides the other sides proportionally,” or, “Similar triangles are to each other as the squares of the homologous sides.” In all my experience I have not received from a pupil a satisfactory explanation of the truth that one divided by infinity is equal to zero, a conception used in secondary mathematics. The same is true of college mathematics. Few students who have studied Analytical Geometry are able to give the true meaning, for instance, of the equation of the straight line, y = sx + m, i. e., that the ordinate of any point of the straight line is m greater than s times the abscissa of the point. These instances may be multiplied to quite an extent.

scholarly journals Competency approach to the study of the second-order surface interface as the geometric location of points in space

2021 ◽  
Vol 27 (1) ◽  
pp. 168-173
Author(s):  
Sergey V. Zharov ◽  
Natalia L. Margolina ◽  
Lyudmila B. Medvedeva
Keyword(s):  
Characteristic Property ◽  
Point Of View ◽  
Algebraic Surfaces ◽  
Analytic Geometry ◽  
Analytical Geometry ◽  
Functional Literacy ◽  
Straight Line ◽  
Surfaces In Euclidean Space ◽  
Order Algebraic ◽  
Order Surface

The necessity of the formation of students' functional literacy as a competency approach to the training of future Mathematics teachers is substantiated on the example of studying of one of the topics of analytical geometry. It has been established that a prerequisite for the development of any competency prescribed in the standards of secondary education is the initial existence of a sufficiently new concept of functional literacy for a student of a certain level. The basic literacy comes down to the ability to read, write and express of one's thoughts correctly. Let us consider the issue of functional literacy from the point of view of the pedagogic specialty. Acquaintance with the well-known textbooks of analytic geometry allows us to say that 2nd order algebraic surfaces in Euclidean space are determined in most cases algebraically by means of equations. A constructive approach is also of use – surfaces are obtained by rotating 2nd degree curves around their symmetry axes and by deformation of the resulting surfaces by compression. The metric approach, as it used for 2nd order curves, is restricted only by the formulation of problems to find the certain locus of points in space. The exception is the article Dmitriy Perepyolkin which was published in 1936. In this paper the locus of points in space with the following characteristic property is studied – the ratio of the distance to a given point to the distance to a given straight line is constant. The strait line is assumed not to contain the point. The study is held out in pure geometrical manner – it is done using the method of sections and known loci of points on the surface. In the present article we study the locus of points in space defined by metric relation to a certain set of pairs of points, lines and planes. It is shown that any non-degenerate 2nd order surface can be considered as a certain locus of points of space and this interpretation is not unique.

Microdensitometer—computer correlation analysis of ultrastructural periodicity

1978 ◽  
Vol 36 (2) ◽  
pp. 32-33
Author(s):  
D.R. Ensor ◽  
C.G. Jensen ◽  
J.A. Fillery ◽  
R.J.K. Baker
Keyword(s):  
Correlation Analysis ◽  
Background Noise ◽  
Computer Control ◽  
Optical Diffraction ◽  
Screw Thread ◽  
Straight Line ◽  
Computer Storage ◽  
Correlation Process ◽  
Electron Microscope Image ◽  
Fixed Beam

Because periodicity is a major indicator of structural organisation numerous methods have been devised to demonstrate periodicity masked by background “noise” in the electron microscope image (e.g. photographic image reinforcement, Markham et al, 1964; optical diffraction techniques, Horne, 1977; McIntosh,1974). Computer correlation analysis of a densitometer tracing provides another means of minimising "noise". The correlation process uncovers periodic information by cancelling random elements. The technique is easily executed, the results are readily interpreted and the computer removes tedium, lends accuracy and assists in impartiality.A scanning densitometer was adapted to allow computer control of the scan and to give direct computer storage of the data. A photographic transparency of the image to be scanned is mounted on a stage coupled directly to an accurate screw thread driven by a stepping motor. The stage is moved so that the fixed beam of the densitometer (which is directed normal to the transparency) traces a straight line along the structure of interest in the image.

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