Abilene High School - Orange and Brown Yearbook (Abilene, KS)

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TWENTY-FOUR g ,.,1 SNAPSHOTS IN THE BUILDING

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completing the square, Q33 The use of a formula developed from solution by square root. In addition to this, a study is made of the features of the equation which determine the nature of the roots. The graph is used, not only as an introduction to the study of equations, but also as a means of relating Algebra to Geometry. Considered in this light, the first degree equation corresponds to the straight line, and the quadratic becomes the Algebraic interpretation of two-dimensional space. The solution of equations by the use of graphs, that is, the determination of points which satisfy the required conditions, gives a new meaning to the locus of Geometry. The object of the course is not to present Algebra as a complete and finished subject, but rather to impress the pupil with the idea that while he has gained enough knowledge to be of valuable assistance, he really has mastered only the a, b, c of mathematics, and that there lies ahead of him a world of thought which will challenge every faculty of mind and imagination to conquer it. PLANE GEOMETRY Geometry is both a mental and a physical science. It is concerned with every- thing which occupies space, for it is the study of forms. In this respect it is the business of Geometry to investigate and classify figures according to their common properties, and to formulate the laws which determine their relationship to each other. From this standpoint Geometry serves to point out the common laws which are in force in all forms of nature. For instance, take the regular hexagon, which may be made up of six triangles, the sides and angles of which are all equal. This figure is the basis for all the various forms of snow-flakes, the cell of the bee is in- variably hexagonalg the blood vessels of the human body under unusual pressure are forced into such a shape that a cross-section takes the shape of a hexagon, and an orchard may be planted to the best advantage by laying out the ground in a series of equilateral triangles with a tree at each vertex. A close observation will discover the fact that wherever in nature conomy of space is needed, the hexagon is the form chosen. Furthermore, Geometrical forms are the basis of architecture, of painting, and in fact, almost every other art, and a knowledge of them is necessary for an aD- preciation of the elements of proportion and symmetry wherever these occur. Ac- cordingly, drawing is an important part of the work in Geometry, as there is no bet- ter method of becoming familiar with the properties of a figure than by constructing it accurately. But Geometry is also a mental science in that the truth of its theorems- is es- tablished not by observation or measurement, but by a rigid process of reasoning, commonly called the demonstration Certain assumptions are made, and on these as a foundation, principles are carefully and logically worked out. Nothing is ad- mitted to be true merely because it looks reasonable, and on the other hand, nothing is accepted contrary to the guidance of common sense merely because a proof con- vincing in appearance has been worked out. From this point of view the object of Geometry is, as it has been for several hundreds of years, to train the brain to an appreciation of clear cut, logical thinking, unprejudiced by feeling. This is not ac- complished, of course, by the mere memorizing of proofs, but rather by original work, so arranged that the argument consists! of but one simple step at first, but gradually becomes more difficult. The demonstration of theorems- given in the text-book is required, in order to see how well the pupils have followed and under- stood the reasoning, but exact reproduction is neither demanded nor encouraged. In fact, some of the more complicated theorems are discussed in class, and the student required to master only certain points of the proof. Numerical exercises, While they do not call for any careful or sustained reasoning on the part of the pupil as a rule, are of value in that they help to make clear and fix in mind the more important theorems, and also show the applicability of the algebraic formula to the work of Geometry. The note book is a feature of the work enjoyed by neither teacher nor pupil, but is useful in that it emphasizes concise, accurate statements and neatly drawn figures. SOLID GEOMETRY The Geometry of two dimensions is studied today before that of three dimen- V TWENTY-THREE

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sions, possibly because it was so developed in the history of the race. The first Geometry was a crude kind of land measurements and it was several hundred years before solids were discovered. WVith the use of drawings only, Solid Geometry rc- quires a more vivid space-imagination than does Plane Geometry, but with actual models of cubes, cylinders and spheres, the work becomes quite simple. The theorems' of Plane Geometry are employed freely, and a large part of the work consists of combining and applying these wherever possible. The content value of Solid Geom- etry is greater as a Whole than that of Plane Geometry. The measurement of sur- faces and volumes is worked out by means of algebraic formulas, and the exerciscs consist to a large extent of applications of these formulas. COMMERCIAL ARITHMETIC The course in Commercial Arithmetic covers one term, and is open to any High School student. 'Ihe primary object is to give practical training and drill to those students who intend to take up commercial work later. The course is not at all technical, however, and the simple business applications made are such as every one should be familiar with. A thorough and systematic review of the fundamental processes-addition, sub- traction, multiplication and division-is given, including whole numbers, common fractions-, and decimals. Abundant drill exercises are furnished through which pupils may learn to deal with numbers accurately and with reasonable speed. Pro- portion, square root, and niensuration, with common business measurements, are discussed later, and application made to practical problems of an industrial nature. The general applications of Arithmetic to business are made under the following topics: Accounts, buying and selling, borrowing, loaning, and investing money, and cancelling indebtedness. lt is not forgotten, however, that before the average per- son invests money, he must save it, and problems dealing with efficient household management are given. The emphasis is laid not so much on the method of solution and results, as on tl1e application of topics to the affairs of the ordinary individual. lt does not mat- ter very much whether or not a pupil knows what the yearly cost of an accumulative bond is, but it may make a great deal of difference to him later if he realizes that a little over S25 of his own money saved and put at interest every year at 6 per cent will amount to S1000 in 20 years. lt causes some amusement to see 10 minutes of labor at the rate of 12c an hour counted in the cost of canning one jar of fruit, but the pupil who works out problems of this kind will come to see that the really ridicu- lous thing is the hap-hazard housekeeping which puts no money value whatever on home labor. A course in Lonimercial Arithmetic cannot train a boy to become an expert business man any more than it can train a girl to become an efficient home maker, but it has accomplished its aim if it teaches boys and girls to have an in- telligent appreciation of efficiency and business management both in making a living and keeping a home. Department of Science GENERAL SCIENCE The Science courses offered in a High School Curriculum have of late become so numerous and specialized that no student can longer hope to cover the whole field. These courses, however, are so inter-related that some knowledge of all is necessary for a mastery of any particular branch. What a beginner in Science should have is an understanding of some of the general principles underlying all the sciences, before attempting to specialize along any particular line. This condition is met by the course offered in Elementary or General Science. While the aim of the course is not to have the student acquire but rather TWENTY-FIVE 2 ' I' E