id: 05877309
dt: j
an: 2011b.01081
au: Kaneko, Masataka; Abe, Takayuki; Fukazawa, Kenji; Sekiguchi, Masayoshi;
Tadokoro, Yuuki; Yamashita, Satoshi; Takato, Setsuo
ti: CAS-aided Visualization in LaTex documents for Mathematical Education.
so: Teach. Math. Comput. Sci. 8, No. 1, 1-18 (2010).
py: 2010
pu: ,
la: EN
cc: R25 K25 U15 U65
ut: LaTex; CAS; accuracy; mathematical expressions; accessories; skeleton;
combinatorial mathematics
ci:
li:
ab: Summary: We have been developing {\it KETpic} as a macro package of a CAS
for drawing fine LaTex-pictures, and we use it efficiently in
mathematical education. Printed materials for mathematics classes are
prepared under several constraints, such as “without animation”,
“mass printings”, “monochrome”, and “without halftone
shadings”. Because of these constraints, visualization in
mathematical education tends to be unsatisfactory. Taking full
advantages of LaTex and CAS, KETpic enables us to provide teaching
materials with figures which are effective for mathematical education.
The effects are summarized as follows: (1) The plottings of KETpic are
accurate due to CAS, and enable students to deduce mathematical laws.
(2) KETpic can provide adequate pictures for students’ various
interest. For example, when some students who understand a matter try
to modify it, KETpic can give them appropriate and experimental
figures. (3) Even though CAS can draw 3D-figures beautifully and
automatically, it is expensive for mass printings and the figures are
sometimes not easy to understand. Oppositely, 3D-graphics by KETpic are
monochrome, but are richly expressive. In this paper, we give various
examples of LaTex-pictures which we drew by using KETpic. For instance,
the picture which is used in order to explain the convergence theorem
of Fourier series makes it easier for students to understand the idea
that function series converge to another function. Also the picture of
skeleton is endowed with clear perspective. KETpic gives us great
potential for the teaching of combinatorial mathematics. Through these
examples, we claim that KETpic should have great possibilities of rich
mathematical expressions under the constraints above mentioned.
rv: