Advanced Abacus: Theory and Practice by Takashi Kojima

By Takashi Kojima

This convenient consultant will take abacus clients from newbie to grasp point in a really brief time.

Though the japanese abacus might seem mysterious or maybe primitive, this exciting device is able to impressive velocity and accuracy. it truly is nonetheless frequent during the store and markets of Asia and its recognition indicates no signal of decline.
This quantity is designed for the coed needing a better figuring out of the abacus and its calculative capabilities. The textual content presents thorough causes of the complex operations concerning damaging numbers, decimals, varied devices of size, and sq. roots. Diagrams illustrate bead manipulation, and various routines supply plentiful practice.
Concise and easy-to-follow, this publication will enhance your abacus talents and assist you practice calculations with larger potency and precision.

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Additional resources for Advanced Abacus: Theory and Practice

Example text

4 + ( -15 16 1112 - -15 64 . i.. n,4 + · · ·) sm '+' ( - 3 n'3 23 n' - 16 . 145) (35 . J.. n, 3 + · · ·) sm '+' + · · · 48 where n' =(a - b)/(a + b), e' 2 = e2 /(l - e 2 ), a, bare semiaxes of the ellipsoid of revolution, and e' is the second eccentricity of the ellipsoid of revolution. 4 Equal-area and equidistant transformations of the ellipsoid onto the surface of a sphere Equal-area transformation This requires that p = mn = 1. 148) Map projections: a reference manual 36 where a, C are constant parameters and R the radius of the equivalent sphere, the type of equal-area transformation depending on how they are determined.

26) 5. 24) it follows that when differentia ls d = 0.

32 11 12 + 64 11 3 + . . 216 + · · ·) sin 2¢ + n'3 - ···}in 6¢ f =(1+ 3 - 152 n13 + .. 1. + . . _ n' 3 + · · ·) sin 6¢ + · · · 192 1 a3 = ( -n' + -31 n12 + · · ·) + (11- + -37 11 12 + · · ·) cos 2¢ 24 96 6 48 12 1 + ( -n + -15 n' 2 + · · ·) cos 4¢ + (n- + · · ·) cos 6¢ + · · · 8 32 48 a4 . /.. 1.. = ( -7 n + -9 ni2 + · · ·) sm '+' I 96 16 12 128 1 . 1. 11 ). 0 1 =D Hence, . I I Perspective transformation of an ellipsoid onto a sphere. where z, z5 P are the arc distances Q0 C on ellipsoid and sphere, respectively.

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