奈良教育大学学術リポジトリNEAR
Course Plan of Mathematics in General
Education 4 credits (2 hours a week and 30 weeks a year)
著者 KUBOTA Isao
journal or
publication title
奈良学芸大学紀要
volume 1
number 3
page range 277‑278
year 1952‑03‑20
URL http://hdl.handle.net/10105/5187
-277- Course Plan of Mathematics in General Education
4 credits (. 2 hours a week and 30 weeks a year ) Isao KUBOTA
Kara Gakugei University
1. How have we tried to devise number and promote the art of calculation?
(1) Natural number, (formation of the idea of
natural number)
(2) Arrangement of thing<. (usage of fingers, decimal system r-systm, number notainn)
(3) Negative number, (the reason for its extnsion) (4) Fraction, (the reason for its extension)
(5) Irrational number, (the reason for its extension, explanations of transcendental number n e ) (6) Complex number, (the r>a on for its extension,
example of its usefulness. )
(7) Addition, (multiplication and definite integral as a special case)
(8) Subtraction, (division :;nd differentiation as a special case )
(9) Usefulness of logarithm (multiplication by ad- dition, division by subtraction, nth root by divis.
ion- nth power by multiplication.)
(10) Utilization of letters, equations and inequalities.
(ll) Utilization of mathematical formulas- ( compound interest, a yearly and monthly payment.) (L2) Utilization of graphs and diagrams.
(13) Calculation by a graphical method.
(14) Utilization of mathematical tools and instrume- nts for calculation (abacus, slide-rule, calculation
machine )
2. On P3Tthagoras and his theorem.
(1) How can we make a right ang'e by means of
a rope?
(2) Pythagorean number ( »;2+n2, 2mn, m~-n%,etc, )
(%) Calculation of square root and the length of
hypotenuse of a right-angled triangle.
(4) Pythagorean proposition and it3 proof in many ways.
(5) Experiments of Pythagorean proportion by means of paper and a knife.
(6) How did Pythagoras find and prove his theo-
rem?
(7) History and achievements of Pythagoras.
(8) Extension of the theorem to other similarities in stead of a square-
(9) Application in Trigonometry.
Sin2/3+Cos2/3=I etc. a2=b2+c2-2bc cosA
Pythagorean theorem in a special case ( i.e.
A=~2 ) of the aboven formula.
(10) Application in Analytic Geometry
VCXj-x2)2 +(y1-y2 j2 distance between
two points.
(ll) Application in Oalculiw
S}/(Ax)2+(Ay)2 *
length of a curved line.
(12) x +y =z does not hold good for any integral
value of n except n=2. This proposition is a subject for one millon dollar prize contest.
3. How do we measure and calculate?
a) I.engths
(1) Various kindb of unit length.
(2) Various scales and tools for thickness and leng- th measurement.
(3) Vernier. Beading of degree by means of the
microscope attached to an inbtrument.
(4) When the equation of a curveis given, we get
the following as the length of a ciuve.
b) Area.
(1) Various kinds of unit area.
(2) Calculation of the area of a simple figure, (triangle, polygon, circle, ellipse)
(3) Calculation of the area by the method of many small block divisions.
(4) When the equation of a figure is given, we get the following 3S the area of a figure.
ja-vdx \ \a ^+P2+'l3 dxdy,etc
(5) Planimeter.
( 6) Surveying instrument. Surveying. Survey map.
Journal of Nara Gakugei University, Vol. I, No. 3. March 20th, 1952
-278- I.KUBOTA
c) Volume
(1) Various units and instruments of volume meas- urement.
( 2) Calculation of the volume of a simple solid body, (tetrahedron, cone, sphere, elliipsoid. ) (3) Calculation of the volume of a solid body.
Weget n\haJ2<ix ^s(x)dx
\ \A F(xy).dxdy, etc.
d) Weight.
(1) Various kinds of unit weight.
(2) Various instilments of weight measurement.
4. How do we tell the correlation by a mathematical method?
a) How do we compare the marks of two subjects.
by means of a graph?
(1) Comparison between original marks of two
subject s.
(2) Comparison between the modified marks of two subjects. (A.M.=100)
(3) Comparison between another modified marki of two subjects. fS.D.=l)
(4) Comparison by means of the correlation figure, b) How do we decide the coefficient o! correlation
which tells the degree of correlation?
(1) Complete Correlation in case of 2(x.-y. )2=0 (2) Complete inverse correlation in ease of
2(x.+y.)2=0
(3) Pearson's coefficient of correlation.
5. How do we represent the shape of a solid body?
(1) Sketch.
^2) Equiangler representation.
( 3) Horizontal-view. Vertical-view- Lateral-view.
(4) The understanding of plans of machines, houses and buildings.
(5) Figure of section.
(6) How do we devise the various patterns mainly on Japanese clothes?
(I) by parallel displacement.
(JI) by revolution.
( Ill) by symmetrical displacement.
(rV) by reflexion. (V )ty balance-.
6. What device has been made in various machines in changing a circular motion into a straight mot- ion?
(1) A sewing-machine.
(2) A printing-machine.
(3) A turning lathe.
(4) Harmonic motion.
(5) Cam.
(6) Periodic motioiif
