Resonance
journal of science education

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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.

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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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Address for Correspondence
C V R Murty
Indian Institute of Technology Kanpur,
Kanpur 208 016, India
Email:eqtips@iitk.ac.in



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