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August 2004
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Classroom

Teaching Chemistry through Riddles
Anindya
Goswami and Imran Habib Biswas
One can use software like Mathematica, Matlab or Maple to plot
a curve or a surface in R^3 whose equations are known. But, since
there is no general method to find equations of a given surface
analytically, we found it interesting to consider some well known
surfaces to find their parametric equations analytically. Here,
in fact, we model those surfaces by exploiting their structural
symmetry. We also provide their plots using Mathematica. We find
that vector algebra is particularly convenient for finding equations.
Read full article ( 1.6 Mb)
Address for Correspondence
Anindya Goswami and Imran Habib Biswas
Department of Mathematics
Indian Institute of Science
Bangalore 560 012, India.
Starting from this issue, Resonance will publish in the Classroom
section, a series of short articles, 'Earthquake Tips', related to earthquakes,
their effects on civil structures, and design and construction of earthquake
resistant buildings. The concepts are clearly explained with sketches
and analogies. We hope the Resonance readers will benefit from this series
of articles.
Earthquake Tips have been brought out by the Department of Civil Engineering,
IIT Kanpur and sponsored by Building Materials and Technology Promotion
Council, New Delhi, India. These articles are reproduced here with permission
from IIT Kanpur and BMTPC, New Delhi.
Learning Earthquake Design
and Construction
1. What Causes Earthquakes?
and
2. How the Ground Shakes!
C V R Murty
The Earth and its Interior
Long time ago, a large collection of material masses coalesced
to form the Earth. Large amount of heat was generated by this
fusion and slowly as the Earth cooled down, the heavier and
denser materials sank to the center and the lighter ones rose
to the top. The differentiated Earth consists of the Inner Core
(radius ~1290km), the Outer Core (thickness ~2200km), the Mantle
(thickness ~2900km) and the Crust (thickness ~5 to 40km). Figure
1 shows these layers. The Inner Core is solid and consists of
heavy metals (e.g., nickel and iron), while the Crust consists
of light materials (e.g., basalts and granites). The Outer Core
is liquid in form and the Mantle has the ability to flow. At
the Core, the temperature is estimated to be ~2500°C, the
pressure ~4 million atmospheres and density ~13.5 gm/cc; this
is in contrast to ~25°C, 1 atmosphere and 1.5 gm/cc on the
surface of the Earth.
The Circulations
Convection currents develop in the viscous Mantle, because
of prevailing high temperature and pressure gradients between
the Crust and the Core, like the convective flow of water when
heated in a beaker (Figure 2). The energy for the above circulations
is derived from the heat produced from the incessant decay of
radioactive elements in the rocks throughout the Earth's interior.
These convection currents result in a circulation of the earth's
mass; hot molten lava comes out and the cold rock mass goes
into the Earth. The mass absorbed eventually melts under high
temperature and pressure and becomes a part of the Mantle, only
to come out again from another location, someday. Many such
local circulations are taking place at different regions underneath
the Earth's surface, leading to different portions of the Earth
undergoing different directions of movements along the surface.
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