Indian Mathematicians & Signal Processing – Contributions of Aryabhata, Bhaskara, and Madhava to trigonometry (core of electronics & communication).

Indian Mathematicians & Signal Processing – Contributions of Aryabhata, Bhaskara, and Madhava to Trigonometry and Communication Theory

Modern electronics and communication systems rely heavily on trigonometry — the mathematical study of angles, waves, and periodic functions. It underpins everything from signal transmission to antenna design and digital signal processing (DSP). What is often overlooked is that many of these foundational trigonometric principles were first formalized by Indian mathematicians more than a millennium ago.

Scholars like Aryabhata (5th century CE), Bhaskara I (7th century CE), and Madhava of Sangamagrama (14th century CE) developed sophisticated mathematical theories of sine, cosine, and infinite series that directly anticipate modern analytical techniques used in electronics today.

Core Insight: The same trigonometric and calculus-based formulas that describe electromagnetic waves, alternating currents, and sound signals in electronics were first explored in ancient India to model planetary motion and cyclical time.

1. Aryabhata (476–550 CE) – The First Systematic Trigonometrical Framework

Aryabhata’s Āryabhaṭīya (499 CE) introduced the earliest known sine (jya) and cosine (kojya) functions. Instead of using chords like the Greeks, he used half-chords (sine), enabling simpler astronomical calculations and early wave modeling.

• Table of Sines: Computed values at 3.75° intervals — similar to modern lookup tables used in DSP algorithms.
• Recursive Formula: Aryabhata described a difference-based method to find successive sines — comparable to iterative signal generation today.
• Wave Concept: His cyclic planetary models established periodicity — the same principle behind alternating current and oscillators.

Parallel to Modern Electronics: Aryabhata’s sine-based models resemble the fundamental representation of AC signals and harmonic motion in circuits.

2. Bhaskara I (600–680 CE) – Accurate Approximation and Analytical Precision

Bhaskara I extended Aryabhata’s work and created the first known rational approximation formula for the sine function, nearly identical in accuracy to modern computational models.

Bhaskara’s Sine Formula:
sin(θ) ≈ [16 × θ × (π − θ)] ÷ [5π² − 4θ(π − θ)]

This formula provides a close approximation of the sine wave across the full range of θ, showing a deep understanding of curve fitting and functional accuracy. In essence, Bhaskara’s work represents a continuous analog version of waveform generation — the same principle used in microcontrollers and DSP processors today.

• Describes smooth, periodic curves mathematically — the base for signal synthesis.
• Minimizes approximation error — a key concept in digital filters.
• Anticipates sine function computation methods used in embedded systems.

Engineering Connection: Bhaskara’s rational approximation is conceptually similar to how digital systems generate sine waves using look-up tables or iterative computation.

3. Madhava of Sangamagrama (1340–1425 CE) – Infinite Series and Waveform Analysis

Madhava, founder of the Kerala School of Mathematics, developed the earliest known infinite series expansions for sine, cosine, and arctangent — forming the groundwork of calculus, centuries before Newton or Leibniz.

Sine series: sin(x) = x − x³/3! + x⁵/5! − x⁷/7! + ...
Cosine series: cos(x) = 1 − x²/2! + x⁴/4! − x⁶/6! + ...

These series accurately describe how periodic motion behaves — and they’re identical to the formulas used in Fourier analysis, the mathematical foundation of all signal processing, modulation, and spectrum analysis today.

Parallel: Madhava’s representation of cyclic motion through infinite series is the same idea used to decompose sound, image, and electromagnetic signals into frequency components.

4. The Mathematical Continuum – From Trigonometry to Signal Theory

Together, Aryabhata, Bhaskara, and Madhava formed the intellectual bridge between ancient astronomy and modern signal processing:

• Periodic Signals: Represented by sine and cosine functions.
• Phase & Frequency: Concepts of angular displacement used in AC analysis.
• Fourier Analysis: Directly parallels Madhava’s infinite expansions.
• Sampling: Bhaskara’s sine approximation mirrors discrete computation.

Engineering Parallel: The trigonometric models of ancient India underpin waveform generators, oscilloscopes, RF transmitters, and modems.

5. Influence on Global Science

Through translations into Arabic and later Latin, India’s jya (sine) became jiba and finally “sinus,” the modern “sine.” The entire terminology of trigonometry carries Indian roots.

The Kerala School’s calculus-like discoveries traveled westward via Jesuit scholars, influencing early European mathematicians and shaping the groundwork of modern calculus — the same mathematics governing electromagnetic theory and electronics.

6. Bridging Ancient Mathematics with Modern Electronics

Every electrical engineer using:

• AC circuits and oscillators
• Amplitude/phase modulation
• Digital filters and FFT analysis
• Signal encoding and decoding

— is applying the same principles first discovered by India’s early mathematicians. Their legacy continues in every sine wave, every modulated signal, and every line of DSP code.

Legacy Summary:

From Aryabhata’s sine tables to Madhava’s infinite series, India’s mathematical brilliance forms the backbone of signal processing and electronics today. Their understanding of periodic motion and waveforms anticipated the mathematics that powers our global communication and digital world.