In actuality, the the fact that Earth's orbit changes hurts your argument. Take the number of seconds in a year vs. the digits of Pi. Right now, the number of seconds in ~0.45% greater than 10,000 Pi. However, since its birth, the sun has been steadily losing mass, which resulted in the Earth moving away slowly. The combined effect is that length of the year has been growing slightly over time. This also means that the number of seconds in a year would have even closer to an even factor of 10,000 larger than Pi than it is now. At the rate the sun loses mass, the point where you get an exact 10,000 to 1 ratio was some 76 million years ago, long before the genus Homo ever appeared on the scene and before the K-T extinction event. As far as eclipses are concerned, the time scale over which they are possible is much larger than a few million years. The angular size of both the Sun and Moon vary due to the eccentricities of both the Earth's and the Moon's orbit. The Sun varies from 31.5-32.5 min of arc and the Moon from 29.33-34 min of arc. For there to be no more total solar eclipses, the Moon would have to recede so that its largest angular size, no longer covered the Sun when it was at it smallest. At the rate the Moon is receding, this is somewhere in the neighborhood of 700 million year from now. Going backwards, you'd have to decide what you would consider the "cut off" point for when the Moon is "too big" to create a "bonfide" solar eclipse. ( at present, when the Sun has its smallest angular size and the Moon its greatest, you can get an eclipse where the Moon is nearly 8% wider than the solar disk, and it still produces a good eclipse. So even if we put the present 8% excess as the limit ( and in reality there's probably some give and take in this.), We were getting total eclipses ~ 1.6 billion years ago. Given the length of time that man has been on the scene, the time scale over which eclipses would be visible is huge (and the age of the Man isn't at the midpoint of this time period. We probably aren't even existing at the "height" of the "eclipse age".