Math
We summarize the week's scientific breakthroughs every Thursday.
- Math
Changes of Mathematical State
Untangling a web of conflicting demands can be tough on computers.
- Math
A Fibonacci Fountain
The year 1202 saw the publication of one of the most famous and influential books in mathematics. Widely copied and imitated, Liber abaci introduced the use of Arabic numerals and the Hindu-Arabic place-valued decimal system into Europe. It was written by Leonardo Pisano, who became better known by his nickname Fibonacci. Helaman Ferguson’s Fibonacci Fountain. […]
- Math
A Fibonacci Fountain
The year 1202 saw the publication of one of the most famous and influential books in mathematics. Widely copied and imitated, Liber abaci introduced the use of Arabic numerals and the Hindu-Arabic place-valued decimal system into Europe. It was written by Leonardo Pisano, who became better known by his nickname Fibonacci. Helaman Ferguson’s Fibonacci Fountain. […]
- Math
Completing Latin Squares
Using only the numbers 1, 2, 3, and 4, arrange four sets of these numbers into a four-by-four array so that no column or row contains the same two numbers. The result is known as a Latin square. Here are two examples of Latin squares of order 4: 1 2 3 4 2 1 4 […]
- Math
Catching Flies
Archerfish and baseball outfielders appear to use different strategies to snag a projectile. Archerfish (Toxotes jaculatrix) are famous for their unusual way of hunting insect prey. Upon spying an insect on a twig or a piece of foliage hanging above the water surface, the fish shoots it down using a strong, accurately aimed jet of […]
- Math
Tilt-A-Whirl Chaos (II)
Tilt-A-Whirl in action. Sellner Manufacturing Co. The Tilt-A-Whirl amusement park ride serves as a wonderful example of a chaotic system. The unpredictable motion of the Tilt-A-Whirl’s cars occurs when the ride’s seven platforms travel at a speed of about 6.5 revolutions per minute along the undulating, circular track (see Tilt-A-Whirl Chaos (I), April 22, 2000). […]
- Math
Tilt-A-Whirl Chaos (I)
Tilt-A-Whirl. Sellner Manufacturing Co. Schematic drawing (top view) showing the Tilt-A-Whirl’s geometry. Much of the fun of an amusement park ride results from its stomach-churning, mind-jangling unpredictability. The Tilt-A-Whirl, for example, spins its passengers in one direction, then another, sometimes hesitating between forays and sometimes swinging abruptly from one motion to another. A rider never […]
- Math
Hiding in DNA
Spies might have to start boning up on molecular biology to pass along and decipher secret messages. During World War II, German spies used microdots to hide information in plain view. Consisting of a greatly reduced photograph of a typed page, a microdot could be pasted on top of a printed period at the end […]
- Math
Hiding in DNA
Spies might have to start boning up on molecular biology to pass along and decipher secret messages. During World War II, German spies used microdots to hide information in plain view. Consisting of a greatly reduced photograph of a typed page, a microdot could be pasted on top of a printed period at the end […]
- Math
Random packing of spheres
A new definition of random packing allows a more consistent and mathematically precise approach to characterizing disordered arrangements of identical spheres.
- Math
Orbiting in a figure-eight loop
Three gravitationally interacting bodies of equal mass can, according to precise calculations, trace out a figure-eight-shape orbit in space.
- Math
Stepping Beyond Fibonacci Numbers
Trying variants of a simple mathematical rule that yields interesting results can lead to additional discoveries and curiosities. The numbers 1, 1, 2, 3, 5, 8, 13, 21, 34, and 55 belong to a famous sequence named for the Italian mathematician Fibonacci, who lived more than 700 years ago. Each consecutive number is the sum […]
