Why did Vāmanadeva ask Bali Mahārāja for three steps of land?

Meanings behind those three steps.

1. Three Steps — Tri-loka

The three worlds are beneath the feet of Krsna. By asking for three steps, Vāmanadeva revealed His position as the Lord of the entire three worlds.

2. Three Steps — Tripāda Vibhūti

In Sanskrit, pāda can mean a division or portion.

Ekāpāda = one-fourth = 25%
Tripāda = three-fourths = 75%

This material universe is Ekāpāda Vibhūti—one-fourth.

Vaikuṇṭha, the spiritual world, is Tripāda Vibhūti—three-fourths.

So the material creation that appears so vast to us is only 25% of the Lord’s total vibhūti, while the spiritual world is 75%.

3. Three Steps — Revealing Viṣṇu

Vāmanadeva was revealing that He is Himself Viṣṇu.

And Viṣṇu means the all-pervading Lord.

Thus, the three steps were not an ordinary request for land.

They revealed three dimensions of Lord:

The three worlds are beneath His feet.
The material world is only one-fourth of His vibhūti.
And He pervades everything.

The Lord was revealing the extent of His own glory.

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