Zero to the power of zero
It is determined by definition that 00 ≝ 1, as you cannot calculate it's value.
Explanation
We start the triangles with 3 balls, and this increases each time with 3 balls.
•
• ••
• •
• • ••
• •
• •
• • • ••
• •
• •
• •
• • • • ••
• •
• •
• •
• •
• • • • • •1 × 3 = 3 2 × 3 = 6 3 × 3 = 9 4 × 3 = 12 5 × 3 = 15
This creates the times table of 3. You can imagine to start with 1 ball. But 0 × 3 = 0 and that doesn't fit in the multiplication table. You can however describe this development with the formula
Number of balls = n × 3 + 0n
There you get for zero 0 × 3 + 00 = 0 + 1 = 1 and that is beautiful.