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When a player is reduced to three pieces, there is no longer a limitation on that player of moving to only adjacent points: The player's men may "fly" (or "hop",[4][5] or "jump"[6]) from any point to any vacant point.

This variant (also called ten men's morris) was invented by Emanuel Lasker, chess world champion from 1894 to 1921. It is based on the rules of nine men's morris, but there are two differences: each player gets ten pieces; and pieces can be moved in the first phase already. This means each player can choose to either place a new piece or to move one of the player's pieces already on the board. This variant is more complex than nine men's morris, and draws are less likely.[14]

Nine men's morris is a strategy board game for two players dating at least to the Roman Empire.[1] The game is also known as nine-man morris, mill, mills, the mill game, merels, merrills, merelles, marelles, morelles, and ninepenny marl[2] in English. In North America, the game has also been called cowboy checkers, and its board is sometimes printed on the back of checkerboards. Nine men's morris is a solved game, that is, a game whose optimal strategy has been calculated. It has been shown that with perfect play from both players, the game results in a draw.[3]

The game might have been played by the sculptors while they were building the huge temples. Inscriptions are seen in many places, carved on stone. The game peaked in popularity in medieval England.[4] A brick found on a mediaeval site near Wisbech, had been used by the brickmakers as a board before being fired.[17] Boards have been found carved into the cloister seats at the English cathedrals at Canterbury, Gloucester, Norwich, Salisbury and Westminster Abbey.[13] These boards used holes, not lines, to represent the nine spaces on the board—hence the name "nine holes"—and forming a diagonal row did not win the game.[18] Another board is carved into the base of a pillar in Chester Cathedral in Chester.[19] Giant outdoor boards were sometimes cut into village greens. In Shakespeare's 16th century work A Midsummer Night's Dream, Titania refers to such a board: "The nine men's morris is filled up with mud".[20]

Twelve men's morris adds four diagonal lines to the board and gives each player twelve pieces. This means the board can be filled in the placement stage; if this happens the game is a draw. This variation on the game is popular amongst rural youth in South Africa where it is known as morabaraba and is now recognized as a sport in that country. H. J. R. Murray also calls the game "the larger merels".

Six men's morris gives each player six pieces and is played without the outer square of the board for nine men's morris. Flying is not permitted.[13] The game was popular in Italy, France and England during the Middle Ages but was obsolete by 1600.[13]

Three men's morris, also called nine-holes, is played on the points of a grid of 2×2 squares, or in the squares of a grid of 3×3 squares, as in tic-tac-toe. The game is for two players; each player has three men. The players put one man on the board in each of their first three plays, winning if a mill is formed (as in tic-tac-toe). After that, each player moves one of the player's men, according to one of the following rules versions:

At the beginning of the game, it is more important to place pieces in versatile locations rather than to try to form mills immediately and make the mistake of concentrating one's pieces in one area of the board.[11] An ideal position, which typically results in a win, allows a player to shuttle one piece back and forth between two mills, removing a piece every turn.

This board is also used for five men's morris (also called smaller merels). Seven men's morris uses this board with a cross in the center.

Some rules sources say this is the way the game is played,[5][6] some treat it as a variation,[4][7][8][9] and some do not mention it at all.[10] A 19th-century games manual calls this the "truly rustic mode of playing the game".[4] Flying was introduced to compensate when the weaker side is one man away from losing the game.

The Latin word merellus means 'gamepiece', which may have been corrupted in English to 'morris',[1] while miles is Latin for soldier.

The board consists of a grid with twenty-four intersections, or points. Each player has nine pieces, or men, usually coloured black and white. Players try to form 'mills'—three of their own men lined horizontally or vertically—allowing a player to remove an opponent's man from the game. A player wins by reducing the opponent to two men (whereupon they can no longer form mills and thus are unable to win) or by leaving them without a legal move.

A mill, however, is better suited to machined parts that are not entirely cylindrical, have flat, complex features, or have offset/angled holes. Mills can machine cylindrical features but if the part is purely cylindrical, then a lathe is a better, more precise option. More complex machines like Swiss lathes can cut flat features and drill perpendicular holes into the material. However, these machines are still better suited to parts that are generally cylindrical.Â

From the above summaries, it should be clear when comparing a mill versus a lathe that lathes are best suited to making cylindrical parts. The cross-section of the part must be round and the same central axis must run through its entire length.

The variety of modern manufacturing machines can be overwhelming. This article will focus on two of the most common categories of machines and compare the uses of a mill versus a lathe. These machines are subtractive manufacturing workhorses and are available in many different configurations.

One of the earliest mentions of the game may be in Ovid's Ars Amatoria.[1][13] In book III (c. 8 CE), after discussing latrones, a popular board game, Ovid wrote:

Strategy millreview

Berger believes the game was "probably well known by the Romans", as there are many boards on Roman buildings, even though dating them is impossible because the buildings "have been easily accessible" since they were built. It is possible that the Romans were introduced to the game via trade routes, but this cannot be proven.[1]

There is another game divided into as many parts as there are months in the year. A table has three pieces on either side; the winner must get all the pieces in a straight line. It is a bad thing for a woman not to know how to play, for love often comes into being during play.

In some European countries, the design of the board was given special significance as a symbol of protection from evil.[1]

Players continue to alternate moves, this time moving a man to an adjacent point each turn. A piece may not "jump" another piece. Players continue to try to form mills and remove the opponent's pieces as in phase one. If all a player's pieces get blocked in (where they are unable to move to an adjacent, empty space) that player loses. A player can "break" a mill by moving a piece out of an existing mill, then moving it back to form the same mill a second time (or any number of times), each time removing one of the opponent's men. The act of removing an opponent's man is sometimes called "pounding" the opponent. When one player has been reduced to three men, phase three begins.

There are many different configurations, but the most common allows the operator to move the part left and right along the X-axis and back and forth along the Y-axis. The cutting tool moves up and down along the Z-axis. A CNC mill can simultaneously control the motion along these axes to create complex geometries like curved surfaces. This primary type of mill is known as a 3-axis mill.Â

Most modern machine shops have both lathes and mills to cover all machining requirements. These machines should not be seen as competitors; they are best used in tandem to cover each other's limitations.

According to R. C. Bell, the earliest known board for the game includes diagonal lines and was "cut into the roofing slabs of the temple at Kurna in Egypt"; he estimated a date for them of c. 1400 BCE.[13] Friedrich Berger wrote that some of the diagrams at Kurna include Coptic crosses, however, making it "doubtful" that the diagrams date to 1400 BCE. Berger concluded: "Certainly they cannot be dated."[1] However, these Coptic crosses themselves certainly are dated no earlier than 42CE according to Coptic Orthodox tradition, very near the end of the known architectural development of the temple.[15] On the other hand, the earliest known board for the game certainly can be dated before the Common Era,[16] as this article shall explain subsequently.

More advanced lathes have automatic tool changers, part catchers for serialized production, and live tools to allow for some milling functionality. For a basic lathe, the setup is relatively simple. The material needs to be secured in the chuck and, in some cases, have its tailstock supported. Programming CNC lathe operations is also relatively simple as there are not many axes. Lathes are good at making cylindrical parts with very tight tolerances and repeatability. Lathes are not used for parts where the primary features are off-axis. Parts with off-axis features cannot be turned on a lathe without additional tooling. For example, a lathe can only drill holes on the central axis by mounting a drill bit in the tailstock; off-center holes are not generally possible in a standard turning operation. Live tooling lathes and Swiss turning machines can do off-axis operations by incorporating drilling and milling operations on their tool holder.

The game begins with an empty board. The players determine who plays first and then take turns. During the first phase, a player's turn consists of placing a man from the player's hand onto an empty point. If a player is able to place three pieces on contiguous points in a straight line, vertically or horizontally, they have formed a mill, which allows them to remove one of the opponent's pieces from the board. A piece in an opponent's mill, however, can be removed only if no other pieces are available. After all men have been placed, phase two begins.

Gold milling

A lathe manufactures cylindrical parts by spinning the material against a fixed tool. Using a lathe to create a part is called turning. The raw stock material is secured in a chuck which is spun at a high rate - this rotational axis is called the C-axis. A lathe's cutting tool is mounted on a tool holder that can move both parallel to the C-axis (denoted as motion along the Z-axis) and perpendicular to the C-axis (X-axis movement). On CNC lathes, complex cylindrical geometries can be turned by controlling the tool holders' X and Z positions simultaneously while varying the rotational speed for certain features.Â

As with lathes, mills come in many different configurations. Variations such as 5-axis mills can cut more complex parts without creating additional workholding solutions to hit the side or off-angle features. A mill can machine a wide range of parts and include many different features that wouldn't work on a lathe. On the flip side, a mill can be complex to set up and program. The part may need to have its orientation changed multiple times to machine all the features. Different setups are called milling operations, or ops, with increased operations adding cost and overhead to a part's manufacture.

Some authors say the game's origin is uncertain.[4] It has been speculated that its name may be related to Morris dances, and hence to Moorish, but according to Daniel King, "the word 'morris' has nothing to do with the old English dance of the same name. It comes from the Latin word merellus, which means a counter or gaming piece."[10] King also notes that the game was popular among Roman soldiers.