Elementary Trigonometry Research Articles

Mathematics Textbooks: Introductory College Mathematics . Chester George Jaeger and Harold Maile Bacon. Harper, New York, ed. 2, 1962. xvii + 423 pp. Illus. $6.50.; Elementary and Advanced Trigonometry . Kenneth S. Miller and John B. Walsh. Harper, New York, 1962. xi + 350 pp. Illus. $5.75.; Analytic Geometry: A Vector Approach . Charles Wexler. Addison- Wesley, Reading, Mass., 1962.

Mathematics Textbooks: <i>Introductory College Mathematics</i> . Chester George Jaeger and Harold Maile Bacon. Harper, New York, ed. 2, 1962. xvii + 423 pp. Illus. $6.50.; <i>Elementary and Advanced Trigonometry</i> . Kenneth S. Miller and John B. Walsh. Harper, New York, 1962. xi + 350 pp. Illus. $5.75.; <i>Analytic Geometry: A Vector Approach</i> . Charles Wexler. Addison- Wesley, Reading, Mass., 1962.

Fibonacci Sequences and a Geometrical Paradox

(1962). Fibonacci Sequences and a Geometrical Paradox. Mathematics Magazine: Vol. 35, No. 1, pp. 1-11.

Trigonometric solution from apparent dip

The apparent‐dip problem may be solved easily, quickly, and accurately by elementary trigonometry.

Aplicações da Trigonometria Esférica em problemas da Simetria Cristalográfica

The present article deals with the application of elementary spherical trigonometry to solution of symmetry problems. The main purpose of the article is to point out symmetry axis associations, and to show the possibilities and impossibilities of several associations, revealed through spherical trigonometric relations. The following axis associations have been a matter of study : a ) 6 + 6; b ) 4 + 4; c ) 2 + 2; d ) 6 + 3; e ) 6 + 4; f ) 6 + 2; g ) 4 + 3. For solution of all the proposed problem sonly one trigonometric formula has been used: cos a = cos b cos c + sen b sen c cos A which is applicable to scalene triangles

Escribed Circles

Escribed circles have disappeared from modern texts in trigonometry in this conntry. Hence many teachers of high school mathematics have college credits in edution, calculus, statistics, and other subjects, but have never heard of escribed circles. This is unfortunate since a study of these circles offers an excellent opportunity to introduce more algebraic work in the trigonometry classes and to give a geometric interpretation of many of the terms that occur in certain formulas. The most thorough treatment of the topic is in Hall and Knight's Elementary Trigonometry (Macmillan Co. of London) but this is now a rare book.

Sign, and Elementary Vector ideas, in Plane Analytical Geometry and Trigonometry.

Plane Analytical Geometry, and elementary Trigonometry, are the beginnings of the systematic application of mathematical analysis to Geometry, i.e. of systematic expression in terms of “number”—which is essentially “real” number.Complete application of the generality of the algebra (within the restriction to real number) is, of course, the power of the method; and, in particular, sign of the (real) numbers is significant throughout.

Fun for the Mathematics Club

With the teachers carrying a war-time load, the mathematics club is apt to die for lack of anything interesting to do. There just isn't sufficient time for the instructor to make the necessary preparations to keep everything going. The literature intended to be helpful is often so general that its value is lost. Some of the literature appears in the nature of a preachment. This wastes almost as much time as the articles which quibble over “objectives.” To give them something specific to do, it is suggested that mathematics clubs, as a part of their activity, build an interesting and useful calculator which will acquaint them with much elementary algebra and trigonometry. It does not require logarithmic scales and can be drawn with an ordinary straight edge and compass with a satisfactory degree of accuracy.

1740. A problem in elementary trigonometry

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1717. A point in elementary trigonometry

1717. A point in elementary trigonometry

Mathematics

MR. BAKST'S mathematics do not go beyond elementary trigonometry and kinetics, so his book is not likely to attract adult readers outside the teaching profession. But a good many children would find it a real help with their elementary arithmetic, algebra, and geometry, and would pick up a fair amount of elementary physics while doing so. Mr. Bakst reverses the usual order of presentation by beginning with an example and deducing the principle concerned. Thus geometric series are introduced by chain letters and Australian rabbits, kinetics by graphs of railway time-tables, and so on. The whole book is interlarded with jokes, a few of which are good. It would be a valuable addition to most school libraries. But if I were a mathematical master I should recommend my brighter pupils to read Hogben's “Mathematics for the Million”, and offer a prize for finding the largest number of mistakes in “Mathematics, its Magic and Mastery”. I have detected them on pages 68, 327, and 638, and I expect there are plenty more. Perhaps there is a negative correlation between wisecracking and accuracy. Mathematics Its Magic and Mastery. By Aaron Bakst. Pp. xiv + 790. (London : Chapman and Hall, Ltd., 1941.) 21s. net.

Mathematics

TEACHERS of elementary trigonometry may discuss the order in which to introduce the tangent, the cosine, and the sine, and there are substantial and interesting arguments in favour of each as the first to be studied, but there has been general agreement for many years that in a first course the tangent and the sine or cosine should be introduced separately, whether the actual definitions are in terms of right-angled triangles or of co-ordinates. It is typical of the teaching of Messrs. Hughes and Miller that they throw the six circular functions simultaneously at the pupil's head at the very beginning, and this implies, on the kindest interpretation, that the subject has been deferred far beyond the age at which the elements of it can profitably be studied. We need scarcely give other reasons for doubting whether this text-book is suitable for the use for which it is intended. On principle, the inclusion of a chapter on spherical trigonometry is to be commended, and an attractive set of tables is paged independently at the end of the volume. The printing and production are exceptionally good. Trigonometry, with Tables Prof. Howard K. Hughes Glen T. Miller By. Pp. viii + 190 + 79. (New York: John Wiley and Sons, Inc.; London: Chapman and Hall, Ltd., 1938.) 7s. 6d. net.

A Modern Elementary Trigonometry. By W S.Catto and F. J. H. Williams. Pp. 263. 3s. 6d. 1936. (Harrap)

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Satellite Station Tables

IT sometimes happens in minor triangulation that well-marked objects, which are otherwise suitable as trigonometrical points, cannot be observed from, though they are well placed for ‘observing to’. Burma, with its innumerable pagodas, offers thousands of examples of this, and it is not surprising that the book under review should have been written by the port surveyor at Rangoon. These tables will save labour in cases in which there is much satellite-station work, though in ordinary minor triangulation, in which satellite stations are usually avoided, or are but rarely used, the surveyor may prefer to make his corrections by the application of elementary trigonometry.

Elementary Trigonometry

IN this volume the authors “have tried to recapture the spirit of some of the writers of a few generations ago who looked on Trigonometry as a branch of applied rather than of pure mathematics”. The course mapped out is therefore different in many ways from that found in most other textbooks. Great stress is laid on “the kind of calculations and manipulations of trigonometric expressions that occur in the applications of the subject”. Theory is not neglected, but it only enters where it is necessary to establish practical formulæ. The scope is fairly wide and includes an excellent section on mensuration and solid geometry. A welcome feature is the introduction of radian measure at the beginning.

Elementary Trigonometry. By J. Prescott and H. V Lowry. Pp. xi, 444. 5s. 1932. (Longmans)

Elementary Trigonometry. By J. Prescott and H. V Lowry. Pp. xi, 444. 5s. 1932. (Longmans)

The Correlation of Elementary Trigonometry and Geometry in Elementary School Mathematics

1. The title of my paper is, perhaps, a little misleading. The word Elementary is intended to apply to the word Mathematics, not to the word School, and I will keep strictly to Elementary Mathematics.The treatment of Geometry in feigned independence of numerical measurement was theoretically abandoned as soon as the supremacy of Euclid collapsed under the onslaught of Professor Perry in the year 1901, and gradually, largely through the efforts of a few outstanding educationists, the teaching of School Geometry in this country has undergone a very remarkable change.

(1) An Elementary Treatise on Actuarial Mathematics (2) Some Recent Researches in the Theory of Statistics and Actuarial Science (3) Probabilités et statistiques

(1) MATHEMATICS has been indebted to actuaries in the past for many valuable contributions in the fields of interpolation, finite differences, and statistical method. We have here an excellent treatise, by an actuary, on those branches of mathematics which are needed by the actuarial student. The author has held in mind the standard required to pass the examinations of the Institute of Actuaries, but has interpreted this standard in a broad way, with the result that we have chapters on elementary trigonometry, on functions and limits, and on differential and integral calculus, as well as those more especially required by the actuarial student, as are the chapters on differences, interpolation, approximate integration, and probability. The result is a model textbook. Proofs are clearly explained, and followed up by many illustrative examples, while the chapters end with a large number of well-chosen examples for solution by the student. (1) An Elementary Treatise on Actuarial Mathematics. By Harry Freeman. (Published for the Institute of Actuaries.) Pp. xiii + 399. (Cambridge: At the University Press, 1931.) 25s. net. (2) Some Recent Researches in the Theory of Statistics and Actuarial Science. By Prof. J. F. Steffensen. (Published for the Institute of Actuaries.) Pp. vi + 52. (Cambridge: At the University Press, 1930.) 5s. net. (3) Probabilites et statistiques. Dr. R. de Montessus de Ballore. (Lecons professes a I'Office National Meteorologique de France.) Pp. ix + 211. (Paris: Hermannet Cie, 1931.) 60 francs.

The “Pellian Equation” and Some Series for π

§ 1. The craze for extensive π-calculation which was so strange a feature of the last century was probably brought to an end not so much by the famous 707 decimals of W. Shanks in 1873 as by the demonstrations of Hermite and Lindemann, about the same time, regarding the transcendental nature of both e and π. Sporadic minor outbreaks of the disease still occur, of course, —Ramanujan in his earlier days was not entirely immune—and the series of the present note may seem symptomatic. It is hoped, however, that they will not be devoid of interest from the point of view of elementary trigonometry.

Elementary Trigonometry. By C. V. Durell and R. M. Wright. Pp. xviii + 288. Tables. Pp. 31. Answers. Pp. xxiv. 5s., or in three parts, price 2s. each. Parts I and II bound together, 3s. 6d. 1929. (G. Bell and Sons Ltd.)

Elementary Trigonometry. By C. V. Durell and R. M. Wright. Pp. xviii + 288. Tables. Pp. 31. Answers. Pp. xxiv. 5s., or in three parts, price 2s. each. Parts I and II bound together, 3s. 6d. 1929. (G. Bell and Sons Ltd.) - Volume 15 Issue 207

Plane Trigonometry

THIS is, in general, quite a well-written book, though, in some respects, on old lines. It covers elementary trigonometry to the logarithmic solution of triangles, and makes a good beginning by defining the functions of angles of any magnitude with the aid of co-ordinates. Circular measure is also developed early and used frequently throughout the text. If, however, it is deemed necessary to devote a section to the theory and practical use of logarithms, there seems no reason for deferring such to the last chapter, especially when logarithms are freely used from Chapter ii. onwards. The section on the linear equation a cosθ + b sinθ = c is not wholly satisfactory. Greater emphasis should be laid on the introduction of irrelevant roots by squaring than is given in Ex. 2 on p. 108. The method of transforming to a quadratic in tan ½θ does not seem to be dealt with.