The rabbit problem | NZ Maths (2024)

FAQs

What is the rabbit math problem? ›

Fibonacci first described his 'famous' number sequence as the solution to a math problem: If a pair of rabbits are put together under certain conditions (“NO Rabbits may leave the field”), how many will there be in one year? This puzzle, posed by Fibonacci in the 13th-century, is the premise for Gravett's book.

Fn+1=Fn+Fn−1. Table 2.1: Fibonacci's rabbit population. 1,1,2,3,5,8,13,21,34,55,89,144,233,… where F13=233 is the solution to Fibonacci's puzzle.

Summary: This is a representation of the classic Fibonacci problem of reproducing rabbits. The problem of how many pairs of rabbits will you have after 1 year if you start with 1 pair and they each take 1 month to mature and produce 1 other pair each month afterwards is illustrated through a calendar.

Fibonacci sequence, the sequence of numbers 1, 1, 2, 3, 5, 8, 13, 21, …, each of which, after the second, is the sum of the two previous numbers; that is, the nth Fibonacci number F_n = F_{n − 1} + F_{n − 2}.

Perhaps the most famous of the paradoxes of infinity, Hilbert's Hotel is a thought experiment where a hotel has an infinite number of rooms, all of which are occupied. Yet, it can still accommodate additional guests, simply by moving them around in a clever way.

The problems consist of the Riemann hypothesis, Poincaré conjecture, Hodge conjecture, Swinnerton-Dyer Conjecture, solution of the Navier-Stokes equations, formulation of Yang-Mills theory, and determination of whether NP-problems are actually P-problems.

The rabbit equation becomes drdt=αr−βrp. If the fox population size p remained constant, this harvesting by the foxes is strikingly similar to your initial harvesting strategy, where a fixed fraction were harvested each month.

The rabbit population problem we're exploring is a variation of the Fibonacci sequence. In the original problem formulated by Fibonacci, each pair of rabbits produces another pair every month. This forms the basic recursive structure: each term is the sum of the previous two.

History. Many sources claim this sequence was first discovered or "invented" by Leonardo Fibonacci. The Italian mathematician, who was born around A.D. 1170, was initially known as Leonardo of Pisa.

Rabbit Rule: Applied vertically, between a claim and each of its reasons, and is combined with the Holding Hands rule. “You can't pull a rabbit out of a hat.” Using these two rules for each simple argument, you make sure that every term mentioned in each box is found in one of the others.

How many rabbits did Fibonacci have in a year? ›

At the end of a year, Fibonacci has 144 pairs of rabbits.

The golden ratio is 1.618, represented by the Greek letter 'phi', is said to be is a mathematical connection between two aspects of an object. It is also called the Fibonacci sequence and it can be found across all of nature: plants, animals, weather structures, star systems – it is ever-present in the universe.

These numbers are used in various fields such as architecture, art, space exploration, engineering, technology, and computing. The Fibonacci sequence, also known as the golden ratio, is utilized in architectural designs, creating aesthetically pleasing structures ¹.

The golden ratio, also known as the golden number, golden proportion, or the divine proportion, is a ratio between two numbers that equals approximately 1.618. Usually written as the Greek letter phi, it is strongly associated with the Fibonacci sequence, a series of numbers wherein each number is added to the last.

The Fibonacci sequence is important for many reasons. In nature, the numbers and ratios in the sequence can be found in the patterns of petals of flowers, the whorls of a pine cone, and the leaves on stems. As the sequence continues, the ratios of the terms approach a number known as the golden ratio.

Here are some theories behind the superstition. At the first of the month, you may notice people saying “rabbit rabbit." That's because of a superstition that if your first words that day are “rabbit rabbit,” you'll have luck for the rest of the month.

Although rabbits were used for all manner of research, the “rabbit test” became synonymous with pregnancy screenings, and the phrase “the rabbit died” entered common usage as a euphemistic way of saying someone was pregnant (even though the rabbit always died during the test).

By following this process, we find that the number of different ways Leo can climb 10 stairs is 89.