1.618 = The Golden Ratio

[HerefordSire]

Thank-you for helping me. If I learned anything on these boards, it would be based upon the following paragraph. The remaining paragraphs are what I am leaving you with in return (I wonder what type of protein these people will consume).

“Nature has this great tendency of balancing things out and reaching a very harmonious equilibrium. If nature were left alone, equilibrium would exist and populations would remain close to them.”

“Tomorrow there will be 260,000 more people on the planet. In the year 3400, we will have a shocking world population of 10 sextillion people. Well before that, the amount of land per person will have dropped to less than one square inch. These incredible numbers illustrate that perpetual physical growth is impossible on a finite planet.”

“It has been calculated that the human population is currently increasing by two percent each year. This is a much more rapid increase than has ever occurred in the history of the planet. Especially high rates of population increase occur in India, China, and selected African countries. It is clear that population growth must stop sometime within the foreseeable future due to various factors. Among these factors are limited food and water supplies, limited energy and natural resources, pollution, animal and plant extinction, and the contamination and scarcity of many other much needed materials. The two elements that regulate population growth are birth and death rates. The question then is whether a slow down in population growth will be a result of a decrease in births or an increase in deaths. If the population continues to grow without bound, nature will take over and the death rate will rise to solve the problem. Unfortunately, this is not the most attractive solution for us. Instead, we would rather control the number of births in order to attack the source of this world problem and save the Earth from being over-capacitated.”

"Long ago in India, according to legend, the inventor of the game of chess so delighted his king that the king asked him to choose one of a number of princely rewards. The inventor bowed and modestly declined, murmuring that he would be happy if the monarch would allow him some wheat to feed his family. He asked that the monarch place one grain of wheat on the first square on his chessboard, two on the second, and double the award for each additional square. The monarch smiled and eager complied, calling for his steward to bring the grain. A chessboard consists of 64 squares. How many grains of wheat did the inventor request?”

“A certain man put a pair of rabbits in a place surrounded on all sides by a wall. How many pairs of rabbits can be produced from that pair in a year if it is supposed that every month each pair begets a new pair, which from the second month on becomes productive?”

“If a cow produces her first calf at age two and produces another single female calf every year, how many female calves are there after 13 years, assuming none die, and each female calf calves at year two?”