The Golden Ratio, also known as the Divine Proportion, is an irrational number approximately equal to 1.618. It is often found in nature and art as it creates a sense of visual harmony and balance.

Indian art and architecture often incorporate various geometric patterns, including the Fibonacci Sequence, Fractal Patterns, and Tessellations. These patterns add visual interest and complexity to the artwork.

The Mandala is a complex geometric design that holds deep spiritual significance in Indian culture. It represents the concept of infinity, is based on the principles of sacred geometry, and often incorporates fractal patterns.

In Indian classical dance, the Tala refers to the rhythmic cycle that governs the dancer's movements. It is a mathematical pattern that determines the number of beats and the duration of each beat.

The Shulba Sutras primarily discuss the Pythagorean Theorem, which relates the lengths of the sides of a right triangle. This knowledge was used in the construction of altars and other religious structures to ensure accurate measurements and proportions.

Fractal Patterns are based on the concept of self-similarity, where a pattern repeats itself at different scales. These patterns are often found in nature and are used in Indian art and design to create intricate and visually appealing motifs.

Vastu Shastra aims to promote energy flow and harmony in a building by considering factors such as orientation, placement of rooms, and the use of specific materials. It is believed that following these principles creates a positive and balanced environment for occupants.

Rangoli patterns often incorporate geometric shapes, symmetry, and principles of sacred geometry. They may also represent mathematical concepts like infinity and fractals, adding depth and meaning to the artwork.

The concept of Raga in Indian music is based on specific mathematical ratios and intervals, follows a mathematical progression of notes, and incorporates mathematical patterns in its rhythmic structure. These mathematical principles contribute to the unique melodic and emotional qualities of a Raga.

Aryabhata, an Indian mathematician and astronomer, is credited with developing a formula for calculating the circumference of a circle. His formula, which states that the circumference of a circle is equal to the diameter multiplied by pi, is still used today.

The Paisley pattern in Indian textile design draws inspiration from various mathematical concepts. It incorporates elements of the Fibonacci Sequence, fractal patterns, and the Golden Ratio, resulting in a visually striking and intricate design.

Jadau jewelry design employs various mathematical principles, including symmetry and balance, geometric patterns, and fractal designs. These principles contribute to the overall beauty and harmony of the jewelry pieces.

Kolam patterns often incorporate geometric shapes, symmetry and balance, and fractal patterns. These mathematical concepts add depth and complexity to the artwork, making each Kolam unique and visually appealing.

The construction of a Shikhara involves the application of various mathematical principles, including the Pythagorean Theorem, Golden Ratio, and Fibonacci Sequence. These principles contribute to the structural stability, aesthetic appeal, and symbolic significance of the Shikhara.

The Nataraja statue exhibits mathematical concepts such as symmetry and balance, geometric proportions, and fractal patterns. These principles contribute to the overall beauty, grace, and symbolic significance of the statue.