Concept: Grids and Fractals in Traditional Indian Architecture
Traditional Indian architecture, especially temple design, is strongly influenced by geometry, symbolism, and cosmological beliefs. Two major design principles commonly observed are the use of grids and fractals. These principles create structural harmony, spiritual meaning, and visual balance in architectural forms.
1. Use of Grids in Indian Architecture
Grids serve as the foundational planning system in many traditional Indian structures, particularly temples and ancient cities. They provide order, proportion, and spiritual alignment.
Through this geometric planning, architecture becomes both functional and spiritually meaningful.
2. Use of Fractals in Temple Design
Fractals refer to repeating patterns that appear similar at different scales. This concept is naturally reflected in many traditional Indian temples.
Fractal patterns enrich temples with both artistic beauty and symbolic depth.
Significance of Grids and Fractals
Conclusion
In traditional Indian temple architecture, grids provide structural order, sacred alignment, and spatial balance, while fractals introduce intricate repetition and symbolic meaning. Together, they create architectural forms that are mathematically precise, spiritually significant, and visually captivating.
A racing track is built around an elliptical ground whose equation is given by \[ 9x^2 + 16y^2 = 144 \] The width of the track is \(3\) m as shown. Based on the given information answer the following: 
(i) Express \(y\) as a function of \(x\) from the given equation of ellipse.
(ii) Integrate the function obtained in (i) with respect to \(x\).
(iii)(a) Find the area of the region enclosed within the elliptical ground excluding the track using integration.
OR
(iii)(b) Write the coordinates of the points \(P\) and \(Q\) where the outer edge of the track cuts \(x\)-axis and \(y\)-axis in first quadrant and find the area of triangle formed by points \(P,O,Q\).