Road signs are an integral part of roads and order on them. It's hard to imagine life without them. And recently I thought about where they came from, who and how they came up with.
But first things first.
First signs
There are many hypotheses about the very first pointers. It is believed that primitive people made routes through forests and open areas, leaving small piles of stone, making notches in trees or breaking branches.
Not the best option. Marks, branches and stones are not always visible.
Next step
Further, people decided to put up pillars with sculpted heads of gods, statesmen and philosophers so that they contrast with natural landscapes. Over time, inscriptions of settlements were added to the signs.
Officially, the first system of road signs originated in ancient Rome. Cylindrical milestones were installed on the roads. They had information about the distance from the Roman Forum, where the golden milestone was located. Therefore, "all roads lead to Rome."
From there, the milestone system spread everywhere. Although our signs appeared rather late: only in the time of Peter I.
New push
The first rules of the road in the modern sense appeared in Portugal in 1686. In the narrow streets of Lisbon, priority signs were installed to regulate traffic flows.
Road signs began to be installed on a large scale for fast and quiet cyclists in the 1870s. Signposts did not contain distance information, but warned, for example, of steep hills.
With the development of the automotive industry, it was decided to revise the system of road signs. In 1895, the Italian Tourist Club completed the development of the first. In 1903, the first signs were installed in Paris.
Standardization failed.
And then it began. Who is into what. Each country had its own road signs. However, car traffic to other states has become commonplace. There was an urgent need to introduce signs of international significance.
So, in Paris in 1909, the following road signs were adopted by the "International Convention on the Movement of Automobiles": "Rough road", "Winding road", "Crossroads", "Intersection with the railway".
Since 1926, international road signs have been intensively developed, they have been changed and supplemented. But whatever one may say, the signs in different countries are different. In some Chinese or Japanese, nothing can be understood at all without knowing the language.
Who invented them
Road signs were not invented overnight. They have evolved and modified over the years.
Understandable to all different types of pointers were developed by more than one person. This work involved automotive users and government committees to create easy-to-read signs. In any case, a focus group is needed, and traffic rules are no exception.
A final touch of humor
Today it is very popular to stick different people, animals and other things on the signs, giving them a cheerful and extraordinary look. I know for sure that there are many of them in Italy.
And depending on the area, the signs can warn about wildlife that run out onto the road: moose, bears, kiwis, crocodiles, penguins and other animals. Plus there are funny ones, like “you can’t go to the toilet in a big way in the forest”, “reproductive zone, don’t interfere with kangaroos” or “you can’t hunt killer whales” in the desert.
So it goes. Have you noticed unusual signs in other countries?
From the Indian icons shown in the bottom line (1st century AD inscription), modern numerals are descended.
To designate numbers from 1 to 9 in India from the 6th century BC. e. the spelling "brahmi" was used, with separate characters for each digit. Somewhat modified, these icons have become modern numbers, which we call Arabic, and the Arabs themselves Indian .
The decimal point, which separates the fractional part of a number from the integer, was introduced by the Italian astronomer Magini (1592) and Napier (1617). Previously, other characters were used instead of a comma - a vertical bar: 3|62, or a zero in brackets: 3 (0) 62
"Two-story" record of an ordinary fraction (for example) was used by ancient Greek mathematicians, although the denominator was written as a denominator, and there was no line of the fraction. Indian mathematicians have moved the numerator up; through the Arabs, this format was adopted in Europe. The fractional line was first introduced in Europe by Leonardo of Pisa (1202), but it came into use only with the support of Johann Widmann (1489).
The plus and minus signs were apparently invented in the German mathematical school of "kossists" (that is, algebraists). They are used in Johann Widmann's textbook A Quick and Pleasant Account for All Merchants, published in 1489. Prior to this, addition was denoted by the letter p(plus) or the Latin word et(conjunction "and"), and subtraction - by the letter m(minus)
The multiplication sign was introduced in 1631 by William Ootred (England) in the form of an oblique cross. Before him, the letter M was most often used, although other designations were also proposed: a rectangle symbol (Erigon, 1634), an asterisk (Johann Rahn, 1659). Later, Leibniz replaced the cross with a dot (end of the 17th century) so as not to confuse it with the letter x; before him, such symbolism was found in Regiomontanus (XV century) and the English scientist Thomas Harriot (1560-1621).
Division signs. Owtred preferred the slash. Colon division began to denote Leibniz.
The plus-minus sign appeared in Girard (1626) and Oughtred. True, Girard also wrote the words “or” between plus and minus.
Exponentiation. The modern record of the exponent was introduced by Descartes in his "Geometry" (1637), however, only for natural powers greater than 2.
The sum sign was introduced by Euler in 1755.
The sign of the product was introduced by Gauss in 1812.
letter ias imaginary unit code:proposed by Euler (1777), who took the first letter of the word imaginarius (imaginary) for this.
The notation for the absolute value and the modulus of a complex number appeared with Weierstrass in 1841. In 1903, Lorentz used the same symbolism for the length of a vector.
=
First printed appearance of the equals sign (equation written)
The equal sign was proposed by Robert Record in 1557.
The “approximately equal” sign was invented by the German mathematician S. Günther in 1882.
The "not equal" sign is first encountered by Euler.
The author of the sign "identically equals" is Bernhard Riemann (1857). The same symbol, at the suggestion of Gauss, is used in number theory as a modulo comparison sign, and in logic as a sign of the equivalence operation.
Comparison marks were introduced by Thomas Harriot in his work, published posthumously in 1631. Before him they wrote: more, less.
The non-strict comparison symbols were proposed by Wallis in 1670.
The symbols "angle" and "perpendicular" were invented in 1634 by the French mathematician Pierre Erigon. Erigon's angle symbol resembled a badge, and was given its modern form by William Oughtred (1657).
Modern designations of angular units (degrees, minutes, seconds) are found in Ptolemy's Almagest.Radian measure of angles, more convenient for analysis , proposed in 1714 by an English mathematician Roger Coats. The term itself radianinvented in 1873 by James Thomson, brother of the famous physicist Lord Kelvin.
The generally accepted designation for the number 3.14159 ... was first formed by William Jones in 1706, taking the first letter of the words Greek. περιφρεια is the circle and περμετρος is the perimeter, i.e. the circumference of the circle. This reduction pleased Euler, whose works fixed the designation completely.
The abbreviated notation for sine and cosine was introduced by Ootred in the middle of the 17th century.
Abbreviations for tangent and cotangent: introduced by Johann Bernoulli in the 18th century, they became widespread in Germany and Russia. In other countries, the names of these functions are used, proposed by Albert Girard even earlier, at the beginning of the 17th century.
Manner of notating inverse trigonometric functions with a prefix arc(from lat. arcus, arc) appeared with the Austrian mathematician Karl Scherfer (German. Karl Scherffer; 1716-1783) and gained a foothold thanks to Lagrange. It was meant that, for example, the usual sine allows you to find the chord subtending it along the arc of a circle, and the inverse function solves the opposite problem. Until the end of the 19th century, the English and German mathematical schools offered other designations: but they did not take root.
The symbol for the partial derivative was first introduced into general use by Carl Jacobi (1837) and then by Weierstrass, although this notation had already appeared earlier in a work by Legendre (1786).
The symbol of the limit appeared in 1787 with Simon Lhuillier and was supported by Cauchy (1821) . The limit value of the argument was first indicated separately, after the symbollim, not below it. Weierstrass introduced a designation close to the modern one, but instead of the usual arrow, he used the equal sign . The arrow appeared at the beginning of the 20th century in several mathematicians at once - for example, in Hardy (1908).
The symbol for this differential operator was coined by William Rowan Hamilton (1853), and the name "nabla" was suggested by Heaviside (1892).
freely available on the Internet
http://goo.gl/WcU0Ss
It is unlikely that among the Internet audience there will be a person who is unfamiliar with this @ symbol. On the web, it is used as a separator between username and hostname in email address syntax.
Some figures in the Internet space call this symbol "one of the main pop symbols of our time, a sign of our common communication space." Somewhat grandiloquently, in my opinion, but the following fact testifies to the worldwide recognition of this symbol, and as it is even sometimes noted, “canonization”.
In February 2004, the International Telecommunication Union introduced a code for the @ character ( - - - ) in Morse code, to facilitate the transmission of email addresses. The code combines the Latin letters A and C and reflects their joint graphic writing.
The search for the origins of the @ symbol takes us back at least to the 15th century, and perhaps even further, although linguists and paleographers still disagree on this issue.
Professor Giorgio Stabile put forward such a hypothesis. A 16th-century document written by a Florentine merchant mentioned "the price of one A of wine" (possibly an amphorae). At the same time, the letter A, according to the then tradition, was decorated with a curl and looked like @.
The American scholar Berthold Ullman suggested that the @ sign was invented by medieval monks to shorten the Latin word "ad", which was often used as a universal word meaning "on", "in", "in relation", etc. In the script used by the monks, the letter "d" was written with a small tail, and this made it look a bit like the number "6" in a mirror image. So the preposition "ad" became the symbol @.
Be that as it may, this innovation was soon adopted by merchants: one of the first to use the symbol outside the walls of the monastery was the Florentine merchant Francesco Lapi, who in one of his letters designated an amphora as a “dog”, a standard measure of volume in those days, approximately equal to 26 -ty l.
In Spanish, Portuguese, French, the name of the symbol comes from the word "arroba" - an old Spanish measure of weight, approx. 15 kg. (according to other sources, 11.502 kg), which was abbreviated on the letter with the @ sign.
During the Renaissance, the @ sign began to be used to indicate the price, but during the Industrial Revolution, the @ sign began to appear in the reports of accountants. The modern official name for the symbol "commercial at" comes from bills, for example, 7 widgets @ $2 each = $14, which translates to 7 widgets. 2$ = 14$. Since this symbol was used in business, it was placed on the keyboards of typewriters and from there migrated to the computer.
We owe the distribution of this symbol on the network to the forefather of e-mail, Tomlinson. He was the one who chose the @ symbol.
Here we need to digress a bit and enlighten you about what Tomlinson did and why it is he who is considered to be the inventor of email, and at the same time the @ sign, when in fact he did neither. The company where Tomltson worked became a member of the ARPANet project, a computer network for the US Department of Defense, around the late 1960s. This network was the forerunner of the Internet. In those years, there were already several programs that were able to transfer a file or message from one person to another. But the sender and recipient needed to use the same computer. As for the modem, even the fastest at that time worked about 200 times slower than a modern conventional one, which allows you to download information at a speed of 56.6 Kbps.
Tomlinson was just at that time developing a mail program and creating a virtual mailbox. In fact, the email box of that time was a file that differed from the usual one in only one feature - users did not have the opportunity to correct the sent text, but only add something of their own. In such an operation, only two programs were used - SNDMSG in order to send the file and READMAIL in order to read it.
Tomlinson also wrote a new program, which consisted of 200 lines of code. Such a program was a cross between the above two programs and the CPYNET protocol, which was used on the ARPANet to send files to a remote computer. Tomlinson's first experimental message was sent from one computer in the lab to another.
In order to forward the file, Tomlinson spent about six months until he managed to send a message to a computer that could indeed be considered remote.
Of course, not very many people knew about Tomlinson's success, only a circle of colleagues, since the merit was not covered anywhere.
Well, now you can return to the "dog". Tomlinson used a 33 Teletype keyboard. And one day he needed a fairly unique symbol that had not been widely used before. Such a character was not supposed to appear in any name or name, and it also had to separate the username and computer name. An algorithm should have been obtained according to the type of name - symbol - place.
In addition to numbers and letters, there were punctuation marks on the keyboard, as well as @. But after 1971, the keyboard model has changed.
@ was the simplest solution to such an algorithm. According to Tomlinson himself, this was the only option. When asked much later why he chose this particular icon, he replied simply: "I was looking on the keyboard for a character that could not appear in any name and cause confusion."
Clickable
In 1963, the ASCII standard encoding appeared, among the 95 printed characters of which there was also a “dog”, and in 1973, members of the Internet Engineering Taskforce secured the use of a character when separating a name and domain - this idea in 1971 th year put forward by the programmer Ray Tomlinson.
Such a symbol was needed by Tomlinson at the time when he was working on the creation of a messaging system in the Arpanet network (the progenitor of the Internet). In essence, he had to come up with a new addressing scheme that would identify not only the recipients, but also the computers on which their mailboxes were located. To do this, Tomlinson needed a separator, and his, in general, random choice fell on the @ sign.
The first network address was [email protected] The mass "dog" became in 1996, when the Hotmail service appeared.
About a year after the events described above, Vintan Cerf and Bob Kahn invented a protocol called TCP/IP. And this was also mentioned for a long time only in narrow circles.
In general, the history of the Internet is quite recent, all historical figures are still alive, so it would be fair to mention the people who had a hand in creating e-mail.
One of the creators is Douglas Engelbart (here is the story of this invention). He made a computer mouse and created the first text messaging system. After that, Tomlinson presented it in the form of an envelope with the field of the recipient, sender and address and the text of the letter. After that, the program was processed by Lawrence Roberts, who came up with a list of letters, reading the letter selectively and saving the information in a separate file and forwarding.
Tomlinson, it should be noted, was quite amused by the hype that unfolded on the 30th e-mail.
Despite the fame that has fallen on him, he comes across as an ordinary person, although he chuckles at the fact that e-mail, according to everyone else, appeared in one day. And it wasn't 30 years ago either. The history of the @ sign is a rather funny epic that is connected with the first message. There are two legends about this.
The first version of what was contained in the historic first letter was that Tomlinson typed QWERTYUIOP - that is, the entire top row of letters from left to right. On this occasion, journalists raised a lot of noise. They were interested in what was written, and clearly expected something significant and symbolic. Since Tomlinson was by no means a public person, he did not realize that he could say anything.
He quite honestly answered about the body of the letter, since he did not suspect at all that it could turn out to be historical. But journalists need zest, not platitudes. Therefore, I didn’t really want to tell everyone that the letter turned out to be a random set of letters. Therefore, QWERTYUIOP appeared. And the engineer does not think to refute this version.
And the second version is that he wrote a quote from Lincoln's Gettysburg speech. One must think that the scientist is simply teasing journalists to the fullest and scoffing as best he can. It would be strange if he actually wrote something sublime in every experimental letter. But the journalists liked this version enough, and they began to repeat it.
In Russia, users most often refer to the “@” symbol as a “dog”, which is why e-mail addresses formed from personal names and surnames sometimes take on unexpected coloring. It is curious that this symbol is used in their work by both folk talents (for example, the joke: “The dog is gone, @ do not offer”), and official jokes - KVN players (for example, “ [email protected]»).
But still: why "dog"? There are several versions of the origin of this funny name.
First, the badge really looks like a curled up dog.
Secondly, the abrupt sound of the English “at” is a bit like a dog barking.
Thirdly, with a fair amount of imagination, you can consider almost all the letters included in the word “dog” in the outlines of the symbol, well, perhaps, with the exception of “k”.
But the most romantic is the following legend: “Once upon a time, when computers were large and displays were exclusively text, there was a popular game with the simple name “Adventure” (“Adventure”). Its meaning was to travel through a computer-generated labyrinth in search of treasures and battles with harmful underground creatures. At the same time, the labyrinth on the screen was drawn with the symbols "!", "+" and "-", and the player, treasures and hostile monsters were indicated by various letters and icons. Moreover, according to the plot, the player had a faithful assistant - a dog who could be sent to the catacombs for reconnaissance. And it was denoted, of course, by the @ sign.
Whether this was the root cause of the now generally accepted name, or, conversely, the icon was chosen because it was already called that, the legend is silent about this.
In fairness, it should be noted that in Russia a “dog” is also called a dog, a frog, a bun, an ear, a ram, and even a kryakozyabra.
In other countries, this symbol is associated with different objects. The following is a far from complete list of how the "@" symbol is called in other countries.
Italians say “chiocciola” (“snail”), in Greece it is known as “παπακι” - “duck”, in the Czech Republic and Slovakia - “zavináč” -rollmops - (“herring roll” or marinated herring), in Taiwan use the concept "小老鼠" (pronounced "xiao lao shu") - "mouse", in Israel the name "שטרודל" - "strudel" is common, and in Kazakhstan the sign is called "aiқұlaқ" - "ear of the moon".
Bulgaria - klomba or maimunsko a ("monkey A"),
Netherlands - apenstaartje ("monkey's tail"),
Spain - like the measure of weight "arroba",
France - the same measure of weight "arrobase",
Germany, Poland - monkey tail, monkey ear, paper clip, monkey,
Denmark, Norway, Sweden - "snabel-a" - "snout a" or elephant trunk,
America, Finland - cat,
China, Taiwan - mouse,
Turkey - rose,
in Serbia - "crazy A",
in Vietnam - "twisted A",
in Ukraine - “ravlik” (snail), “doggie” or, again, “dog”.
As you can see, for many nations, the @ sign evokes an association with a snuggly animal, for some with an appetizing strudel or herring roll, the poetic Turks compared it with a flower, but the disciplined Japanese use the English “attomark” without any poetic comparisons.
sources
http://www.factroom.ru/facts/40864#more-40864
http://shkolazhizni.ru/archive/0/n-7999/
http://viva-woman.ru/novosti-so-vsego-sveta/kak-pojavilsja-simvol-sobaka.html
÷ Subtraction There is an opinion that the signs "+" and "-" originated in trading practice. The vintner marked with dashes how many measures of wine he sold from the barrel. Pouring new reserves into the barrel, he crossed out as many expendable lines as he restored the measures. So, supposedly, there were signs of addition and subtraction in the 15th century. The inverted Greek letter psi Ψ was used in Greece to denote subtraction in the 3rd century BC. Italian mathematicians used the letter m, the initial letter in the word minus, to do this. In the 16th century, the “-” sign began to be used to indicate the action of subtraction, and in the 17th century, minus began to be denoted by the sign ÷ to distinguish minus from a dash. This sign is found in the Russian mathematician Leonty Magnitsky at the beginning of the 18th century in his book Arithmetic. In L. Magnitsky's book, subtraction examples looked like this: 6 ÷ 2 15 ÷ 12 Leonty Filippovich Magnitsky ()
Division: For thousands of years, the action of division was not indicated by signs. It was simply called and written down in words. Indian mathematicians were the first to designate division by the initial letter from the name of this action - D. The Arabs introduced a line to indicate division. It was adopted from the Arabs in the 13th century by the Italian mathematician Fibonacci. He was the first to use the term "private". The colon sign (:) for division began to be used at the end of the 17th century. Before that, such a sign was also used ÷ In Russia, the names “divisible”, “divisor”, “private” were first introduced by Leonty Magnitsky at the beginning of the 18th century. Mathematicians of the Middle Ages.
Ordinary fraction The first fractions that history introduces us to are fractions of the form: ½; 1/3; ¼ - unit fractions These fractions originated 2000 years ago. Archimedes had other fractions, numbers. We call them mixed. In Russian, the word "fraction" appeared in the 8th century, it came from the verb "crush" - to break into pieces. In the first mathematics textbooks, fractions were called “broken numbers”. The modern designation of fractions originates in ancient India. At first, the fractional line was not used in the notation of fractions. The fraction feature only came into use around 300 years ago. In 1202, the Italian merchant Fibonacci (gg.) introduced the word "fraction". The names "numerator" and "denominator" were introduced in the 13th century by Maxim Planud - a Greek monk, scientist, mathematician. In Western Europe, the theory of ordinary fractions was given in 1585 by the Flemish engineer Simon Stevin. Simon Stevin (gg.) Archimedes (about 287 - -212 BC)
% Percent This word in Latin means "per hundred". Interest was especially common in ancient Rome. The Romans called interest the money that the debtor paid for every hundred. For a long time, interest was understood as profit or loss for every hundred rubles. They were used only in commercial and monetary transactions. Then they began to be used both in science and in technology. There are two opinions about the percent sign. 1. The% sign comes from the Italian word "cento" (one hundred), which was abbreviated cto. In calculations, this word was written very quickly, and gradually the letter t turned into a slash, a symbol appeared to denote a percentage. 2. The percent sign is due to a typo. In 1685, a book on arithmetic was printed in Paris, where by mistake the typesetter typed % instead of cto. After this error, many mathematicians began to use the % sign to represent percentages. Gradually, this sign gained universal recognition. Robert Record, English mathematician, physician. (1510 - 1558)
Equality \u003d The equal sign was designated at different times in different ways: both in words and symbols. The sign “=”, which is very understandable for us, was introduced in 1557 by the English mathematician and physician Robert Record. This is how he explained the choice of sign. "No two objects can be more equal to each other than two parallel lines" This sign came into general use only in the 18th century, thanks to the German mathematician Wilhelm Leibniz. Drawing for the book on mathematics by Robert Record "Castle of Knowledge"
Multiplication To denote the action of multiplication, European mathematicians of the 16th century used the letter M, which was the initial in the Latin word for increase, multiplication, - animation. From this word came the name "cartoon". In the 17th century, some mathematicians began to denote multiplication with a cross, while others used a dot for this. In the 16th and 17th centuries, there was no uniformity in the use of symbols. It wasn't until the late 18th century that most mathematicians used a dot to multiply. William Outred, an English mathematician, introduced the multiplication sign with a cross in 1631. The famous German mathematician of the 17th century, Wilhelm Leibniz, used the dot to denote multiplication. In Europe, for a long time, the product was called the sum of multiplication. The name "multiplier" is mentioned in the works of the 11th century, and "multiplier" in the 13th century. In Russia, Leonty Magnitsky was the first to give names to the components of multiplication at the beginning of the 18th century. Wilhelm Leibniz, German mathematician. (1646 - 1716)
Addition +++ Separate signs for some mathematical concepts appeared in antiquity. However, until the 15th century, there were almost no generally accepted arithmetic signs. In the 15th and 16th centuries, the Latin letter "P", the initial letter of the word "plus", was used for the addition sign. For addition, the Latin word "et", meaning "and", was also used. Since the word “et” had to be written very often, they began to shorten it: first they wrote one letter “t”, which gradually turned into a “+” sign. The ancient Egyptians denoted addition with a sign - a pattern of walking legs. The name "term" first occurs in the works of mathematicians of the 13th century, and the concept of "sum" - in the 15th century. Until that time, the sum was the result of any of the four arithmetic operations. For the first time, the signs "+" and "-" appear in print in the book "A quick and beautiful account for all merchants." It was written by the Czech mathematician Jan Widman in 1489. Mathematician. 15th century
History of the compass
The compass is familiar to every person from school - in drawing lessons one cannot do without this tool for drawing circles and arcs. In addition, it is used to measure distances, for example, on maps, it is used in geometry and for navigation. Usually compasses are made of metal and consist of two "legs", at the end of one of them there is a needle, on the second writing object, usually a graphite stylus. If the compass is measuring, needles are located at both ends.
The word compass itself comes from the Latin circulus - "circle, circumference, circle", from the Latin circus - "circle, hoop, ring." In the Russian language, compasses or compasses came from the Polish cyrkuɫ or the German Zirkel.
Now it is no longer possible to say who exactly invented this instrument - history has not preserved his name for us, but the legends of Ancient Greece attribute authorship to Talos, the nephew of the famous Daedalus, the first "aeronaut" of antiquity. The history of the compass dates back several thousand years - judging by the surviving drawn circles, the instrument was familiar to the Babylonians and Assyrians (II - I centuries BC). On the territory of France, an iron compass (1st century AD) was found in a Gallic burial mound; during excavations in Pompeii, many ancient Roman bronze compasses were found. Moreover, quite modern tools were found in Pompeii: compasses with curved ends for measuring the internal diameters of objects, “calipers” for measuring the maximum diameter, proportional ones for multiplying and decreasing sizes. During excavations in Novgorod, a steel compass-cutter was found for drawing an ornament from small regular circles, which was very common in Ancient Russia.
Over time, the design of the compass has not changed much, but a lot of nozzles have been invented for it, so now it can draw circles from 2 mm to 60 cm, in addition, a regular graphite lead can be replaced with a nozzle with a pen pen for ink drawing. There are several main types of compasses: marking or dividing, it is used to remove and transfer linear dimensions; drawing or circular, it is used to draw circles with a diameter of up to 300 millimeters; drawing caliper for drawing circles from 2 to 80 millimeters in diameter; drawing caliper for drawing circles with a diameter of more than 300 millimeters; proportional - to change the scale of the size being taken.
The compass is used not only in drawing, navigation or cartography - it has also been used in medicine: for example, large and small compasses are used to measure the transverse dimensions of the human body and to measure the size of the skull, respectively, and the compass-caliper is used to measure the thickness of the subcutaneous fat folds. Also known is the compass of Weber, a German psychophysiologist and anatomist, developed by him to determine the threshold of skin sensitivity.
But the compass is not only a well-known tool. This word is called a small constellation of the southern hemisphere to the west of the "Square" and "Southern Triangle", next to the α-Centaurus. Unfortunately, this constellation is not observed on the territory of Russia.
In addition, the compass is a symbol of steady and impartial justice, a perfect figure of a circle with a central point, the source of life. Along with the square, the compass defines the limits and boundaries of a straight line. In ritual architecture, the compass symbolizes transcendent knowledge, the archetype that controls all work, the navigator. In Chinese, the compass means correct behavior. The compass is an attribute of Fo-hi, the legendary Chinese emperor, who was considered immortal. Sister Fo-hi has a square, and together they are the male and female principles, the harmony of yin and yang. Among the Greeks, the compass, along with the globe, was a symbol of Urania, the patroness of astronomy.
A compass combined with a square is one of the most common emblems, symbols and signs of Freemasons. On this emblem, the compass symbolizes the Vault of Heaven, and the square symbolizes the earth. The sky in this case is symbolically connected with the place where the Great Builder of the Universe draws the plan. The letter "G" in the center in one of the meanings is an abbreviation of the word "geometer", used as one of the names of the supreme being.
History of the protractor
Since ancient times, people have faced the need to measure. The concept of a degree and the appearance of the first instruments for measuring angles are associated with the development of civilization in ancient Babylon, although the word degree itself is of Latin origin (degree - from Latin Gradus - “step, step”). A degree is obtained by dividing a circle into 360 parts. The question arises - why did the ancient Babylonians divide exactly into 360 parts. The fact is that in Babylon the sixty-decimal number system was adopted. Moreover, the number 60 was considered sacred. Therefore, all calculations were related to the number 60 (the Babylonian calendar included 360 days).
In addition to the degree, units of measurement such as the minute (part of a degree) and the second (part of a minute) were introduced. The names “minute” and “second” come from partes minutae primae and partes minutae sekundae, which means “smaller first parts” and “smaller second parts”. In the history of science, these units of measurement were preserved thanks to Claudius Ptolemy, who lived in the 2nd century.
History has not preserved the name of the scientist who invented the protractor - perhaps in ancient times this tool had a completely different name. The modern name comes from the French word "TRANSPORTER", which means "to carry". Presumably, the protractor was invented in ancient Babylon.
But ancient scientists made measurements not only with a protractor - after all, this tool was inconvenient for measuring on the ground and solving problems of an applied nature. Namely, applied problems were the main subject of interest of ancient geometers. The invention of the first tool that allows you to measure angles on the ground is associated with the name of the ancient Greek scientist Heron of Alexandria (I century BC). He described the diopter tool, which allows you to measure angles on the ground and solve many applied problems.
Thus, we can talk about the emergence of geodesy - a system of sciences about determining the shape and size of the Earth and about measurements on the earth's surface to display it on plans and maps. Geodesy is associated with astronomy, geophysics, astronautics, cartography, etc., and is widely used in the design and construction of structures, navigable canals, and roads.
A protractor (fr. transporteur, from lat. transporto “I carry”) is a tool for constructing and measuring angles. The protractor consists of a ruler (rectilinear scale) and a semicircle (goniometric scale) divided into degrees from 0 to 180°. In some models - from 0 to 360 °.
Protractors are made of steel, plastic, wood and other materials. The accuracy of a protractor is directly proportional to its size.
Varieties of protractors
Semicircular (180 degrees) - the most simple and ancient protractors.
Round (360 degrees).
Geodetic, which are of two types: TG-A - for building and measuring angles on plans and maps; TG-B - for drawing points on a drawing basis at known angles and distances. The division price of the goniometric scale is 0.5 °, the rectilinear scale is 1 millimeter.
More advanced types of protractors that are needed for more precise constructions and measurements. For example, there are special protractors with a transparent ruler with a goniometric vernier that rotates around the center.
History of mathematical signs
Have you ever thought about where the mathematical signs came from and what they originally meant? The origin of these signs can not always be precisely established.
There is an opinion that the signs "+" and "-" originated in trading practice. The vintner marked with dashes how many measures of wine he sold from the barrel. Pouring new reserves into the barrel, he crossed out as many expendable lines as he restored the measures. So, supposedly, there were signs of addition and subtraction in the 15th century.
There is another explanation regarding the origin of the “+” sign. Instead of "a + b" they wrote "a and b", in Latin "a et b". Since the word “et” (“and”) had to be written very often, they began to abbreviate it: first they wrote one letter t, which, in the end, turned into a “+” sign.
The name “term” is first encountered in the works of mathematicians of the 13th century, and the concept of “sum” received a modern interpretation only in the 15th century. Until that time, it had a broader meaning - the sum was the result of any of the four arithmetic operations.
To denote the operation of multiplication, one of the European mathematicians of the 16th century used the letter M, which was the initial in the Latin word for increase, multiplication, - animation (the name "cartoon" comes from this word). In the 17th century, some mathematicians began to denote multiplication with a slash "×", while others used a period for this.
In Europe, for a long time, the product was called the sum of multiplication. The name "multiplier" is mentioned in the works of the XI century.
For thousands of years, the action of division was not indicated by signs. The Arabs introduced the line "/" to indicate division. It was adopted from the Arabs in the 13th century by the Italian mathematician Fibonacci. He was the first to use the term "private". The colon sign ":" to indicate division came into use at the end of the 17th century. In Russia, the names “divisible”, “divisor”, “private” were first introduced by L.F. Magnitsky at the beginning of the 18th century.
The equal sign was denoted at different times in different ways: both by words and by various symbols. The “=” sign, so convenient and understandable now, came into general use only in the 18th century. And this sign was proposed to denote the equality of two expressions by the English author of the algebra textbook Robert Ricord in 1557.
The plus and minus signs were apparently invented in the German mathematical school of "kossists" (that is, algebraists). They are used in Johannes Widmann's Arithmetic, published in 1489. Prior to this, addition was denoted by the letter p (plus) or the Latin word et (conjunction "and"), and subtraction- letter m (minus). In Widman, the plus symbol replaces not only addition, but also the union "and". The origin of these symbols is unclear, but most likely they were previously used in trading as signs of profit and loss. Both symbols almost instantly gained general acceptance in Europe.- with the exception of Italy, which used the old designations for about a century.
The multiplication sign was introduced in 1631 by William Ootred (England) in the form of an oblique cross. Before him, the letter M was used. Later, Leibniz replaced the cross with a dot (late 17th century) so as not to confuse it with the letter x; before him, such symbolism was found in Regiomontanus (XV century) and the English scientist Thomas Harriot (1560-1621).
Division signs. Owtred preferred the slash. Colon division began to denote Leibniz. Before them, the letter D was also often used. In England and the United States, the ÷ (obelus) symbol, which was proposed by Johann Rahn and John Pell in the middle of the 17th century, became widespread.
The plus-minus sign appeared in Albert Girard (1626) and Oughtred.
The equal sign was proposed by Robert Recorde (1510-1558) in 1557. He explained that there is nothing more equal in the world than two parallel segments of the same length. In continental Europe, the equal sign was introduced by Leibniz.
The "not equal" sign is first encountered by Euler.
Comparison marks were introduced by Thomas Harriot in his work, published posthumously in 1631. Before him, they wrote in words: more, less.
Non-strict comparison symbols were proposed by Wallis. Initially, the bar was above the comparison sign, and not below it, as it is now.
The percent symbol appears in the middle of the 17th century in several sources at once, its origin is unclear. There is a hypothesis that it arose from a compositor's mistake, who typed the abbreviation cto (cento, hundredth) as 0/0. It is more likely that this is a cursive commercial badge that arose about 100 years earlier.
The root sign was first used by the German mathematician Christoph (according to other sources, Thomas) Rudolph, from the Kossist school, in 1525. This character comes from the stylized first letter of the word radix (root). The line above the radical expression was absent at first; it was later introduced by Descartes for a different purpose (instead of brackets), and this feature soon merged with the root sign.
The root symbol of an arbitrary degree began to be used by Albert Girard (1629).
Exponentiation. The modern notation for the exponent was introduced by Descartes in his Geometry (1637), although only for natural powers greater than 2. Newton later extended this form of notation to negative and fractional exponents (1676).
Parentheses appeared in Tartaglia (1556) for the radical expression, but most mathematicians preferred to underline the highlighted expression instead of brackets. Leibniz introduced brackets into general use.
The symbols "angle" and "perpendicular" were invented by the French mathematician Pierre Erigone; however, his perpendicular symbol was reversed, resembling the letter T.
We owe the symbol "parallel" to Oughtred.
The generally accepted notation for the number 3.14159... was formed by William Jones in 1706, taking the first letter of the Greek words περιφέρεια- circumference and περίμετρος- perimeter, that is, the circumference of a circle.
