# Math Is Fun Forum

Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫  π  -¹ ² ³ °

You are not logged in.

## #1 2023-09-11 01:09:19

Jai Ganesh
Registered: 2005-06-28
Posts: 46,437

### Ball

Ball

Gist

A ball is any object in the shape of a sphere, especially one used as a toy by children or in various sports such as tennis and football.

Summary

A ball is a spherical or ovoid object for throwing, hitting, or kicking in various sports and games. The ball is mentioned in the earliest recorded literatures and finds a place in some of the oldest graphic representations of play. It is one of the earliest children’s toys known.

A ball can be made from many different materials, leather, rubber, and synthetics being most common in modern times. However, balls made from indigenous materials, particularly from animal parts, were once the norm. For instance, among the Yahgan (or Yámana) of South America a ball called a kalaka was made from an albatross web (foot) that was blown up and stuffed with goose feathers and sewn. The Yahgan also used an inflated seal stomach as a ball. Among the Navajo of North America, balls were made from buckskin bags filled with seeds and held together by a drawstring.

Some form of ball game is portrayed on early Egyptian monuments. Even among the Romans, who disliked participatory sports, ball play was extremely popular. The Roman baths set aside apartments for ball play, and many gentlemen had ball courts in their private villas. The ancient Roman ball was usually made of leather strips sewn together and filled with various materials. The smallest, the harpastum, was a hard ball stuffed with feathers. The largest, the follis, contained an air-filled bladder, similar to a modern football (soccer ball) or basketball.

In many early games the ball was simply thrown back and forth among individuals in a group, but there were also genuine team games and competitions among the ancient Greeks. Ball games were especially popular at Sparta. One early Greek game known as episkyros involved two teams of equal numbers. Between them a white line was laid out, and, at some distance behind each team, another line was marked. The play consisted in throwing the ball back and forth until one team in the exchange was finally forced back over its rear line. Ball playing also is of great antiquity in western Europe.

An early form of lacrosse was well established among the American Indians in pre-Columbian times. Ball games such as lacrosse were mainly of a religious nature, dedicated to the gods and played to ensure the well-being of the community. Among Native American children, kickball was encouraged by the adults. A Mayan clay figurine from the 8th century AD depicting a ball player wearing protective gloves and hip padding was found in Jaina, Mexico. Ball games were important to the ancient Mayans and other Middle American peoples, and almost all Mayan cities had ball courts—rectangular areas enclosed by tiers of seats for spectators. At heights of 20 to 30 feet (6 to 9 metres), a stone ring through which the ball was to be thrown was set into the wall, in a game known as pok-a-tok or tlachtli. The ball was made of rubber and was approximately 6 inches (15.2 cm) in diameter. Long ball, a traditional ball game still played among the Onondaga peoples of the Iroquois in upstate New York, is a form of tag employing a bat and a ball. Among the Igbo of Nigeria, boys play okpasa, a game in which three boys, with one in back and two in front, must avoid being touched by the ball. In villages in Vietnam, a traditional ball and chopstick game is played by children.

As skills required in games using the ball alone, and more particularly in games involving the use of various implements for striking it, were developed and refined, balls became specialized and were made in a multiplicity of types. The weight and circumference of balls have changed over the years as the other equipment and rules of the individual sports have changed in order to increase the interest of spectators. An example of this is the change made in the American football with the popularization of the forward pass, from the egg-shaped rugby ball to a more elongated shape that was easier to throw with accuracy. This variation changed the sport from a running game to one in which the forward pass played an exciting role.

Details

A ball is a round object (usually spherical, but can sometimes be ovoid) with several uses. It is used in ball games, where the play of the game follows the state of the ball as it is hit, kicked or thrown by players. Balls can also be used for simpler activities, such as catch or juggling. Balls made from hard-wearing materials are used in engineering applications to provide very low friction bearings, known as ball bearings. Black-powder weapons use stone and metal balls as projectiles.

Although many types of balls are today made from rubber, this form was unknown outside the Americas until after the voyages of Columbus. The Spanish were the first Europeans to see the bouncing rubber balls (although solid and not inflated) which were employed most notably in the Mesoamerican ballgame. Balls used in various sports in other parts of the world prior to Columbus were made from other materials such as animal bladders or skins, stuffed with various materials.

As balls are one of the most familiar spherical objects to humans, the word "ball" may refer to or describe spherical or near-spherical objects.

"Ball" is used metaphorically sometimes to denote something spherical or spheroid, e.g., armadillos and human beings curl up into a ball, making a fist into a ball.

Etymology

The first known use of the word ball in English in the sense of a globular body that is played with was in 1205 in Laȝamon's Brut, or Chronicle of Britain in the phrase, "Summe heo driuen balles wide ȝeond Þa feldes." The word came from the Middle English bal (inflected as ball-e, -es, in turn from Old Norse böllr (pronounced [bɔlːr]; compare Old Swedish baller, and Swedish boll) from Proto-Germanic ballu-z (whence probably Middle High German bal, ball-es, Middle Dutch bal), a cognate with Old High German ballo, pallo, Middle High German balle from Proto-Germanic *ballon (weak masculine), and Old High German ballâ, pallâ, Middle High German balle, Proto-Germanic *ballôn (weak feminine). No Old English representative of any of these is known. (The answering forms in Old English would have been beallu, -a, -e—compare bealluc, ballock.) If ball- was native in Germanic, it may have been a cognate with the Latin foll-is in sense of a "thing blown up or inflated." In the later Middle English spelling balle the word coincided graphically with the French balle "ball" and "bale" which has hence been erroneously assumed to be its source. French balle (but not boule) is assumed to be of Germanic origin, itself, however. In Ancient Greek the word (palla) for "ball" is attested besides the word (sfaíra), sphere.

History

A ball, as the essential feature in many forms of gameplay requiring physical exertion, must date from the very earliest times. A rolling object appeals not only to a human baby, but to a kitten and a puppy. Some form of game with a ball is found portrayed on Egyptian monuments. In Homer, Nausicaa was playing at ball with her maidens when Odysseus first saw her in the land of the Phaeacians (Od. vi. 100). And Halios and Laodamas performed before Alcinous and Odysseus with ball play, accompanied with dancing (Od. viii. 370). The most ancient balls in Eurasia have been discovered in Karasahr, China and are 3.000 years old. They were made of hair-filled leather.

Ancient Greeks

Among the ancient Greeks, games with balls  were regarded as a useful subsidiary to the more violent athletic exercises, as a means of keeping the body supple, and rendering it graceful, but were generally left to boys and girls. Of regular rules for the playing of ball games, little trace remains, if there were any such. The names in Greek for various forms, which have come down to us in such works as the Ὀνομαστικόν of Julius Pollux, imply little or nothing of such; thus, (aporraxis) only means the putting of the ball on the ground with the open hand, (ourania), the flinging of the ball in the air to be caught by two or more players; φαινίνδα (phaininda) would seem to be a game of catch played by two or more, where feinting is used as a test of quickness and skill. Pollux (i. x. 104) mentions a game called episkyros, which has often been looked on as the origin of football. It seems to have been played by two sides, arranged in lines; how far there was any form of "goal" seems uncertain. It was impossible to produce a ball that was perfectly spherical; children usually made their own balls by inflating pig's bladders and heating them in the ashes of a fire to make them rounder, although Plato (fl. 420s BC – 340s BC) described "balls which have leather coverings in twelve pieces".

Ancient Romans

Among the Romans, ball games were looked upon as an adjunct to the bath, and were graduated to the age and health of the bathers, and usually a place (sphaeristerium) was set apart for them in the baths (thermae). There appear to have been three types or sizes of ball, the pila, or small ball, used in catching games, the paganica, a heavy ball stuffed with feathers, and the follis, a leather ball filled with air, the largest of the three. This was struck from player to player, who wore a kind of gauntlet on the arm. There was a game known as trigon, played by three players standing in the form of a triangle, and played with the follis, and also one known as harpastum, which seems to imply a "scrimmage" among several players for the ball. These games are known to us through the Romans, though the names are Greek.

Modern ball games

The various modern games played with a ball or balls and subject to rules are treated under their various names, such as polo, cricket, football, etc.

Physics

In sports, many modern balls are pressurized. Some are pressurized at the factory (e.g. tennis, squash) and others are pressurized by users (e.g. volleyball, basketball, football). Almost all pressurized balls gradually leak air. If the ball is factory pressurized, there is usually a rule about whether the ball retains sufficient pressure to remain playable. Depressurized balls lack bounce and are often termed "dead". In extreme cases a dead ball becomes flaccid. If the ball is pressured on use, there are generally rules about how the ball is pressurized before the match, and when (or whether) the ball can be repressurized or replaced.

Due to the ideal gas law, ball pressure is a function of temperature, generally tracking ambient conditions. Softer balls that are struck hard (especially squash balls) increase in temperature due to inelastic collision.

In outdoor sports, wet balls play differently than dry balls. In indoor sports, balls may become damp due to hand sweat. Any form of humidity or dampness will affect a ball's surface friction, which will alter a player's ability to impart spin on the ball. The action required to apply spin to a ball is governed by the physics of angular momentum. Spinning balls travelling through air (technically a fluid) will experience the Magnus effect, which can produce lateral deflections in addition to the normal up-down curvature induced by a combination of wind resistance and gravity.

It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

Offline