By T. Sundara Row
"The From the INTRODUCTION.
the assumption of this e-book was once advised to me by means of Kindergarten reward No. VIII.—Paper-folding. The present contains two hundred variously colored squares of paper, a folder, and diagrams and directions for folding. The paper is colored and glazed on one aspect. The paper may perhaps, besides the fact that, be of self-colour, alike on either side. in truth, any paper of reasonable thickness will solution the aim, yet colored paper exhibits the creases greater, and is extra appealing. The kindergarten present is offered by way of Messrs. Higginbotham and Co.; yet colored paper of either kinds could be had within the bazaars. A packet of a hundred squares of either varieties accompanies this ebook, and the packets is additionally had individually. Any sheet of paper may be minimize right into a sq. as defined within the establishing articles of this ebook, however it is neat and handy to have the squares prepared minimize.
2. those workouts don't require mathematical tools, the one issues worthwhile being a penknife and scraps of paper, the latter getting used for environment off equivalent lengths. The squares are themselves basic substitutes for a directly part and a T sq..
three. In paper-folding numerous vital geometrical techniques might be effected even more simply than with a couple of compasses and ruler, the single tools using that's sanctioned in Euclidian Geometry; for instance, to divide directly strains and angles into or extra equivalent components, to attract perpendiculars and parallels to instantly strains. it really is, notwithstanding, impossible in paper-folding to explain a circle, yet a few issues on a circle, in addition to different curves, could be acquired by way of different tools. those routines don't consist only of drawing geometrical figures regarding directly traces within the traditional approach, and folding upon them, yet they require an clever software of the easy techniques exceptionally, tailored to paper-folding. this may be obvious on the very graduation of this publication.
four. using the kindergarten presents not just provides fascinating occupations to girls and boys, but in addition prepares their minds for the appreciation of technological know-how and paintings. Conversely the instructing of technological know-how and paintings afterward may be made attention-grabbing and dependent upon right foundations through connection with kindergarten occupations. this can be relatively the case with Geometry, which kinds the root of each technology and paintings. The instructing of Euclid in faculties will be made very fascinating by way of the unfastened use of the kindergarten presents. it might be completely valid to require students to fold the diagrams on paper. this may provide them neat and exact figures, and galvanize the reality of the propositions forcibly on their minds. it will no longer be essential to take any assertion on belief. yet what's now realised by means of the mind's eye and idealization of clumsy figures may be obvious within the concrete. A fallacy just like the following will be impossible.....
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Extra resources for Geometric Exercises in Paper Folding
22, on 3: of art. The . / rt . rt. /. three angles at J/, being each equal to TV, and Q of the pentagon remain of a right angle, the 2 ing two angles are together equal to -^ - of a right Therefore each of them angle, and they are equal. is | of a right angle. Therefore all the angles of the pentagon are equal. The pentagon 72. - The 73. is also equilateral by construction. 6180.... greatest breadth of the pentagon If/ be the equal to XB, altitude, is 58. AB. 9510. . =AB cos Fig. 28. 74. if J?
ABCD overlaps the square by the four rectangles AF, BG, Clf, and 48. In Fig. 15, the square EFGH DE. ABCD = (a-\- 2 ) , and IN PAPER FOLDING the square = square EFGH(a ELCM = a 2 . <) 2 . 17 Also square AKGN KBLF = Square square T ft Squares ABCD EFGH are and together equal to the latter four squares put together, or to twice the AKGN square (a + 2 ) -f (a D and twice the square 2 ) = 2a 2 2 4- 2^ KBLF, that is, . O C N Fig. 16. 49. In Fig. 16 the rectangle ( -*). Because the rectangle angle PL = square PK PL is equal to (a-\-ft EK = FM, square AE, therefore rect i.
Cos 20 = %a cos 20 = * X 0. 4698463. 723136. 2 , - VIII. THE DECAGON AND THE DODECAGON 99. Figs. 36, 37 show how a regular decagon, and a regular dodecagon, may be obtained from a penta gon and hexagon respectively. Fig. 36. The main part of the process is to obtain the angles at the center. In Fig. 36, the radius of the inscribed circle of the pentagon is taken for the radius of the circum scribed circle of the decagon, in order to keep within the square.