The Science of AUM — And Geometry Before Pythagoras

Bharat’s rich heritage shows that long before modern science, our sages explored the universe through sound, geometry, and consciousness.

ॐ – the most divine chant that we have known since time immemorial. The chant that we relate to divinity and spirituality. To start with, it's not OM; it's A U M

Do you know that there is a sound of the "heartbeat" of the Earth, and the sound vibration is at a specific frequency?

First proposed by German physicist Winfried Schumann in 1952 and later confirmed experimentally, the Earth’s electromagnetic field is shaped by global lightning activity. These lightning strikes generate waves that become trapped between the Earth’s surface and the ionosphere, forming standing waves known as Schumann resonances. The strongest of these vibrations—at about 7.83 Hz—is often called the planet’s heartbeat or natural tuning fork for life.

When chanted correctly, the vibrations produced by AUM are believed to generate a frequency that can harmonise or synchronise with the Earth's natural frequency of 7.83 Hz. This is the frequency where you connect to nature and the divine, and hence we use ॐ during our prayers.

The 7.83 Hz frequency falls right at the border of the human brain's alpha waves (8−12 Hz) and theta waves (4−8 Hz). Alpha waves are associated with calm, relaxed alertness and a meditative state, and theta waves are linked to deep relaxation, meditation, creativity, and intuition. And the confluence of the two is the core objective of meditation, and hence ॐ is what we chant while meditating.

AUM chanting begins in the abdomen with the “A” sound, rises through the chest and throat with the “U”, and ends with the humming “M” resonating in the crown of the head. This upward vibration is said to energise the body’s chakras, fostering peace and well-being.What scientists uncovered barely 75 years ago has been part of our tradition for millennia. And the wisdom of ancient India didn’t end with sound and vibration — even in mathematics and geometry, our sages showed extraordinary insight long before their Western counterparts.

Ancient Indian geometry

As children, we learnt that the square of a right triangle’s hypotenuse equals the sum of the squares of its other two sides. A principle known as Pythagoras’ Theorem, attributed to the Greek mathematician Pythagoras around 500 BCE.

But centuries earlier, India’s learnt Rishis (Gyaanis) had explored similar concepts and more. The Śulba Sutras—meaning “rules of the cord”—described the geometry and mathematics used to design Vedic fire altars.Among the eight major texts, the oldest is the Baudhayana Śulba Sutra, though the science behind these rituals predates the written records.

In 800 BCE, Rishi Baudhayana had written some of these Sutras.

1. Pythagorean Theorem

Sutra 1.12 - Aksnayā Rajju

दीर्घस्याक्ष्णया रज्जुः पार्श्वमानी, तिर्यग् मानी च यत् पृथग्भूते कुरुतस्तदुभयाङ् करोति।

English Translation:  The rope stretched along the length of the diagonal [of a rectangle] produces an area that the vertical and horizontal sides make together.

Meaning: The area of the square drawn on the diagonal (hypotenuse) is equal to the sum of the areas of the squares drawn on the vertical (length) and horizontal (breadth) sides.

2. Value of the Square Root of 2

Sutra: I.61-62 (Elaborated in Āpastamba Śulbasūtra I.6)

समस्य द्विकरणी। प्रमाणं तृतीयेन वर्धयेत् तच्चतुर्थेनात्मचतुस्त्रिंशोनेन सविशेषः।

English Translation: "The diagonal [dvikaraṇī] of a square. The measure [side length] is to be increased by a third and by a fourth, decreased by the thirty-fourth part [of that fourth]. That is its diagonal approximately."

Formula (implied): If the side of the square is a = 1, the length of the diagonal (\sqrt{2}) is approximately:

1 + 1/3 + 1/(4 × 3) - 1/(34 × 4 × 3)

We may not have been the first—Egyptian and Babylonian scholars also studied these concepts—but the depth of our Rishis’ knowledge is remarkable. Sadly, they are often seen merely as ascetics, when in truth they were profound scholars and scientists.

Whether it’s the hum of AUM resonating with the Earth’s heartbeat or the geometric brilliance of our Rishis, ancient Indian wisdom endures. It reminds us that science and spirituality were never separate — only two paths to the same truth.