MY DISCOVERIES OF BANGALORE

I recently typed "Bangalore" in Google Maps and tried to make some sense of the shape it displayed - perimeter, area, similar looking shapes, specialties and so on (pl see the map below). 

Map of Bangalore

As you can see, the outline doesn't bring to mind any regular shape we know in geometry. There's a vague resemblance with Australia if you view it upside down - otherwise it's  shape is just that of another omelet! So I tried to make  some sense of it and here are a few things that I discovered along the way:

1. Many of us Bangaloreans think that Cubbon Park is the center of Bangalore. Well, that's somewhat correct, but according to the venerable Google Maps, Bangalore's center is (Lat, Long) (12.97159, 77.59456). If you look for details of this point, you'll find it is an office of IBM - IBM India Pvt Ltd D3 Block, Vittal Mallya Rd, Bangalore 560001. Maps' center is about 900 metres from Cubbon Park.

2. Bowing to Maps' choice of center, i.e using  IBM India D3 Block, Vittal Mallya Rd  as center, the biggest contiguous circle within Bangalore (i.e. using innermost border points from the center and excluding the small hatched space below Electronics City) is the one in dark red colour. It's radius is approximately 18.5 km.  Consequently, area and circumference are 1075.2 sq km and 116.2 km respectively. This inner circle passes through Whitefield, Baiyapanahalli, Sathanur, Makali, Thavarekere, Ramohalli, Kumbalgodu & Sompura.

2. The biggest circle that passes through/ close to most of Bangalore's periphery is the one in green colour. It has a radius of 24.3 km (Area=1855 sq km. Circumference=152.7 km).

3. Diagonals:

D1. Alappanahalli (13.078616, 77.797294)  to Maligondanahalli (12.899728, 77.434627) - 44.5 km

D2. Chowdappanahalli(13.140478, 77.747876) to Bidadi (12.803908, 77.401541) - 53.35 km

D3. Hosahalli (13.150505, 77.648733) to K. Chudahalli

(12.775784, 77.489431) - 45.6 km

D4. Ragihalli State Forest (12.743639, 77.559469) to Channahalli (13.175039, 77.614610) - 48.3 km

D5. Kukkanahalli (13.152495, 77.437407) to Sampangere (12.867854, 77.878891) - 57.6 km

D6. Neelamangala(13.116134, 77.385633) to Chandapura (12.801010, 77.713075) - 50km

The average of the above 6 diagonals is 50 km. Hence an imaginary circle that contains  "most of Bangalore" has a radius of 25 km. This agrees well with the result of Srl 2 above.

4. I used Maps' line tool to connect about 200 points along Bangalore's periphery  and found the approximate perimeter to be 249.9 km. An "equivalent" circle would have a radius of about 40 km. An equivalent square would have a side of 62.5 km.

5. As 25 km would be a good estimate of Bangalore's radius, 40 km (from Srl 4 above) is highly exaggerated. This mathematically reinforces our view that Bangalore is extremely bloated, far from any regular geometric shape. 

6. Area, by plotting points taken from Bangalore's border in a graph drawing software tool works out to 1630.5 sq km. This compares very poorly with the 709 sq km estimate given by Wikipedia. Either my estimate or Wiki's needs to be corrected soon.