 
Summary: Mathematics Around Us
There is mathematics all around us; we just have to observe and think about it.
It is hidden in a glass of water, in lamp shades and in tree leaves.
Take a glass of water and
tilt it. What do you see?
Do you notice anything familiar about the shadow cast by a lamp shade?
The mathematician Appolonius of Perga ( born in 262 BC in Perga, modern Antalya in
Turkey) studied the mathematics of these figures. These are conic sections .
Let us see hear in his own words why he studied them `They are worthy of acceptance for
the sake of demonstrations themselves, in the same way as we accept many other things
in mathematics for this and for no other reason'.
But why should you care about these figures.? Here is why:
These figures have remarkable reflection properties. The head lights of your car use this:
the mirror is made from a parabolic surface and the rays emanating from the focus all
become parallel.( Show it).
A modern treatment of kidney stones called lithotripsy uses the reflection properties of
the ellipsoids. Here rays from one focus are reflected back to the other focus. This allows
for safe transport of waves from one point to another.( Show picture with narrative).
Lithotripsy, a medical procedure for treating kidney stones. The patient is placed in a
elliptical tank of water, with the kidney stone at one focus. Highenergy shock waves
