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An evolutionist suggests that at some distant point 400 million years in the past one of his ancestors was an early form of fish. Try to estimate the number of generations that link the scientist to the fish. To make your estimation, you will need to fill in sensible values for the species in the table below (you will possibly need to research these numbers, and feel free to use a spreadsheet for the calculations. A good place to start is http://en.wikipedia.org/wiki/Timeline_of_human_evolution)
Category 
First appearance (million years ago)

Similar modern day example  

Similar modern day creature  Time from birth to producing first offspring  Lifespan (years)  
Bony fishes  400  Coelacanth 


Amphibians 
350

Lungfish 


Reptiles 
300

Lizards 


Early mammals 
200

Small dogs 


Mammals 
75

Lemurs 


Apes  15  Gorillas 


Humans 
1

Charles Darwin  30  73 
Can you produce a sensible estimate for a number that you are confident exceeds the actual number of generations?
Can you produce a sensible estimate for a number that you are confident is definitely less than the actual number of generations?
There will be various estimates and assumptions that you need to make in this question. Can you clearly state the most important factors?
A 1 metre cube has one face on the ground and one face against a wall. A 4 metre ladder leans against the wall and just touches the cube. How high is the top of the ladder above the ground?
The problem is how did Archimedes calculate the lengths of the sides of the polygons which needed him to be able to calculate square roots?