### Archimedes and Numerical Roots

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?

### Interstellar

Weekly Problem 22 - 2012
What number could replace * so that */5 is between 3 and 4?

### More or Less?

Are these estimates of physical quantities accurate?

# Time to Evolve

##### Stage: 4 Challenge Level:

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?

NOTES AND BACKGROUND

Suggested timelines for evolution form fascinating reading.

Interestingly, the bony coelacanth fish was considered extinct by scientists until fishermen caught one alive in 1938. Now they occasionally turn up, caught in deep-water nets.