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If you gave me one of your cows, then we would have the same number of cows.

Ian Stewart's top 10 popular mathematics books

Click here for the answer Farmer Brown has five and Farmer Green has seven cows. I have more than two animals at home. All of them are dogs, except for two.

All of them are cats, except for two. All of them are hamsters, except for two. What kinds of animals and how many of each animal do I have? See the answer I have three animals: A brick weighs one kilogram plus half of the brick. What is the weight of one brick? Here is the answer It weighs 2 kg. Since half a brick weighs 1 kg, the brick weighs 2 kg. A car is going up a hill. The hill is one mile long. The driver goes up the hill at an average speed of 30 miles per hour. When the driver reaches the top of the hill, he starts down the other side.

The downhill side is also one mile long. How fast must the driver go down the hill in order to average 60 miles per hour? Solution It is impossible to average 60 miles per hour. An average speed of 60 miles per hour requires two minutes to cover two miles. The first mile was covered at 30 miles per hour. This means that two minutes were used to travel that mile. Hence there are no minutes left to cover the second mile. There are 7 girls on a bus. Each girl has 7 backpacks. In each backpack, there are 7 big cats.

For every big cat there are 7 little cats. How many legs are on the bus, not counting the driver?

Cones (3-D Shapes)

Solution There are a total of 10, legs. There are 7 girls. They have 14 legs. See the answer 10 hours 70 minutes equals 11 hours 10 minutes. An intelligent trader travels from 1 place to another carrying 3 sacks having 30 coconuts each. No sack can hold more than 30 coconuts.

4. Euclid in the Rainforest by Joseph Mazur

On the way he passes through 30 checkpoints and on each checkpoint he has to give 1 coconut for each sack he is carrying. How many coconuts are left in the end? Solution There are 25 coconuts left. He will give out 3 coconuts at each of the first 10 checkpoints and empty his first bag. He has two sacks left. Then he gives out 2 cocounts at each of the next 15 checkpoints, emptying his second bag.

Then he has one bag of coconuts left and only 5 checkpoints to go, which means he gives out 5 coconuts from the last bag and is left with 25 coconuts. A milkman has an 8-liter container full of milk, and also two empty containers that measure 5 liters and 3 liters. He needs to deliver 4 liters of milk to a customer. The milkman has no other spare containers and no way to mark any containers.

He does not want to pour milk away. How will he measure the 4 liters of milk? Geometry - Math: Kindle Store

Solution Fill the 5-liter container. Pour out from the 5-liter container to the 3-liter one until it's full. The 5-liter container now has 2 liters left. Pour all the milk from the 3-liter container back to the 8-liter container. Pour the 2 liters from the 5-liter container to the 3-liter container. It has therefore just one liter of space left! Fill the 5-liter container. Pour out from the 5-liter container enough milk to fill the 3-liter container which already has 2 liters.

Learn how to make a hexaflexagon and why playing Brussels sprouts is a waste of time. A thoroughly readable account of the meaning of truth in mathematics, presented through a series of quirky adventures in the Greek Islands, the jungles around the Orinoco River, and elsewhere.

Examines tricky concepts like infinity, topology, and probability through tall tales and anecdotes. Three different kinds of truth are examined: The story of the student who believed nothing except his calculator is an object lesson for everyone who thinks mathematics is just 'sums'. In Francis Guthrie, a young South African mathematician, was attempting to colour the counties in a map of England. Guthrie discovered that he needed only four different colours to ensure that any two adjacent counties had different colours.

After some experimentation he convinced himself that the same goes for any map whatsoever. This is the remarkable story of how mathematicians eventually proved he was right, but only with the aid of computers, bringing into question the meaning of "proof". It contains enough detail to be satisfying, but remains accessible and informative throughout.

The classic text What is Mathematics? It answered its title question by example.

The IMPOSSIBLE QUIZ Challenge (Fail) Sibling Tag - Collins Key vs Devan Key

Hersh takes a more philosophical view, based on his experience as a professional mathematician. The common working philosophy of most mathematicians is a kind of vague Platonism: Although this is what it feels like to insiders, Hersh argues that mathematics is a collective human construct — like money or the Supreme Court. However, it is a construct constrained by its own internal logic; it's not arbitrary.

You choose the concepts that interest you, but you don't get to choose how they behave. Both authors are top-rank mathematicians with years of stage performances behind them, and their speciality is mathematical magic.

The best websites with math games, puzzles, and fun math

They show how mathematics relates to juggling and reveal the secrets behind some amazing card tricks. The magician mails a pack of cards to anyone, asking them to shuffle it and choose a card. Then he shuffles the cards again, and mails half of them to the magician—not saying whether the chosen card is included. By return mail, the magician names the selected card. Biologists' understanding of many vital features of the living world, such as sex and survival, depends on the theory of evolution. One of the basic theoretical tools here is the mathematics of game theory, in which several players compete by choosing from a list of possible strategies.

The children's game of rock-paper-scissors is a good example. The book illuminates such questions as how genes spread through a population and the evolution of cooperation, by finding the best strategies for games such as cat and mouse, the battle of the sexes, and the prisoner's dilemma.

A Visual Introduction to the Fourth Dimension (Rectangular 4D Geometry)

On the borderline between popular science and an academic text, but eminently readable without specialist knowledge. A collection of 23 science fiction short stories, each of which centres on mathematics. Two are by Martin Gardner, and many of the great writers of SF are represented: The high point is Norman Kagan's utterly hilarious "The Mathenauts", in which only mathematicians can travel through space, because space is mathematical — and, conversely, anything mathematical can be reality. An isomorphomechanism is essential equipment.

Between them, these tales cover most of the undergraduate mathematics syllabus, though not in examinable form. There ought to be a great classic in this top 10, and there is none greater. I've put it last because it's not popularisation in the strict sense.

However, it slips in because it communicated to the world one of the very greatest ideas of all time: Nature has laws, and they can be expressed in the language of mathematics. Using nothing more complicated than Euclid's geometry, Newton developed his laws of motion and gravity, applying them to the motion of the planets and strange wobbles in the position of the Moon. He famously said that he "stood on the shoulders of giants", and so he did, but this book set the scientific world alight.

As John Maynard Keyes wrote, Newton was a transitional figure of immense stature: