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Sure, startups can and do disrupt established industries, but manufacturing such a complex plane on budget and on time to keep down the price per passenger requires more than entrepreneurial brashness.

He painted this complex plane, with its traceries, sculptures, pilasters and sunken portals jutting out and receding, 28 times, after first painting two close-ups of the Tour Saint Romain, one of the two western towers.

However, Poncelet had no idea that projective geometry would reveal the mysterious nature of zero, because the second important advance, the complex plane, was still needed.

This simple construction, called the complex plane, revealed a lot about the way numbers work.

Multiplication and exponentiation in the complex plane became geometric ideas; you could actually see them happening.