Napier Chip —— How do foreigners "strategize"

As the name implies, Napier chip is a computing chip invented by a man named Napier.

Napier, as a famous mathematician in Scotland, is not very famous. Presumably, most people have never heard of it. However, he invented a mathematical concept, which is the famous logarithm that every high school student can master. It seems that Napier did not name logarithm Napier number. This wave is really a loss.

Napier was born in a landlord family, but he didn't become a silly son as usual. His father is not only a landlord and an official, but also the owner of the Scottish Mint. 16 years old, gave birth to a child. His mother is also a suitable official second generation; Later, this unscrupulous family also created a title of its own-Lord Napier, which won't lose money. ...

As an aristocrat, Napier was taught privately by his family since childhood. He didn't go to primary school. /kloc-at the age of 0/3, he was sent to St. Andrews University. It didn't take long for the university to drop out of school and go to Europe for further study, but no one knows what he studied before he came back at the age of 2 1 (yes, he finished his post-university studies at the age of 2 1); I bought a castle at the age of 24 and lived in it for decades. After my father died at the age of 58, I moved to my father's castle and lived there until I died at the age of 67. Apart from his distinguished family background, Napier's own life really didn't leave many interesting stories.

It seems that he spent his whole life trying to make some contributions in the field of mathematics and went down in history in the last three years of his life.

16 14, 64-year-old Napier published the book Description of the Wonderful Logarithm Table, which became a symbol that human beings obtained logarithms from God. Later generations refer to a special logarithm mentioned in the book as Napier logarithm:

PS: It's good to write a formula with Markdown for the first time. I hope it won't scare away readers who are as afraid of mathematics as I am. ...

With logarithm, multiplication and division can be simplified to addition and subtraction, which greatly reduced the amount of calculation in the scientific community at that time.

Coincidentally, Napier's invention also aims to reduce complex operations such as multiplication and division to addition and subtraction.

16 17, introducing napier's monograph Rabdologi? "[1] was published in Edinburgh, and Napier died smartly at the age of 67, leaving the world with a second precious legacy besides numbers.

Napier chips are made of various materials, such as wood, metal and cardboard. The English name is Napier's bone. Perhaps the earliest use is animal bones (not Napier bones), so it is often called Napier bone chips. Because the shape is a small stick, it is often called Napier stick.

Although it is a calculation, Napier uses an "abacus" to support the calculation. The left boundary of the abacus is marked with 1~9 from top to bottom, corresponding to 9 squares on each computing chip. There are 10 chips, and the squares on the chips are filled with the product of 0~9 and the numbers on the left margin. In short, this is a multiplication table of 99.

Except for the top first square, the next eight squares are diagonal lines, which are used to separate ten digits from single digits. This is done to use an algorithm called dot matrix multiplication (or more vividly shutter multiplication). For example:

Take the four chips of the multiplicand 6, 7, 8 and 5, and look at the eighth line:

With the diagonal as the boundary, each digit is added together, exceeding 9:

This is the simplest multiplication, the steps of division are a little more complicated, and the calculation of root is more complicated. It is also necessary to introduce special new chips, and the specific algorithm is of little significance here. Interested friends can move to Wikipe tan by themselves.

Rabdologi? Having been translated into many languages (including Chinese), Napier potato chips are all the rage. Later, many improvements and variants appeared, such as making the chip into a rotatable cylinder:

This cylindrical Napier chip provided inspiration for the problems of later mechanical calculators. Many pioneers of mechanical calculation, such as William Sikard of Germany, Tito Bratini of Italy, Samuel Moran of Britain and René Geyer of France, all built mechanical calculators based on Napier chips.

In the19th century, Napier was simply made oblique for ease of reading:

After 1628 was introduced into China, various localization deformations also appeared. For example, Mei Wending, a mathematician in Qing Dynasty, changed it into a semicircle instead of a diagonal: