Algorithm for rational determination of the area of a triangle for the development of students' creative thinking and practical application. Properties of the 90 Degrees angle tangent

The article presents the formulas derived by the author for determining the area of a triangle by a side and two adjacent angles. These for - mulas are used to activate the educational process — students in practice figure out how to rationally determine the area of land plots, buildings, draw up and solve trigonometric equations, prove the properties of the tangent of an angle equal to 90 degrees, correct the graph of the function y = tg x. To carry out calculations of the areas of triangles, to prove the properties of 90 degree angle tangent, to solve trigonometric equations, programs are written in the Visual Basic For Application language in Microsoft Word. Using the binary-decimal system and VBA programs in Word, the value of the tangent of an angle is calculated so close to an angle of 90 degrees that this value can be roughly taken as the 90 degrees angle tangent. The study of this material at informatics lessons contributes to the development of creative thinking of students, increasing their motivation to study informatics and information technology.

The fundamental constants of physics and the International System of Units

Air Canada managed to have a passenger aircraft run out of fuel in mid-air due to confusion about metric units (Stephenson in Mars climate orbiter mishap investigation board phase I report, NASA, 1999), and NASA lost an entire spacecraft due to a misunderstanding amongst engineers about the units used in the propulsion system design (Witkin in Jet’s fuel ran out after metric conversion errors, The New York Times, 1983). Measurements only make sense if the units are correct and well-defined. A unit of measurement is a definite magnitude of a quantity, defined by convention or law. Any other quantity of that kind can then be expressed as a multiple or submultiple of the unit of measurement. The Egyptians used the Farao as definite magnitude, while many years later, the french revolutionists introduced the earth as a reference and laid the foundations for the modern decimal system. Since recently, we have a truly universal and stable system that uses physics’s natural constants and laws to define the base units of measurement. This paper explains how this new concept works and how it is implemented in practice.

Method for extracting square and cube roots in the binary number system

The article describes in detail the methods of extracting square and cube roots in the binary number system. The method for extracting the square root of a binary number is similar to the corresponding method for decimal numbers, which is called the "column method". As for decimal numbers, when choosing the next digit of the root, twice the current value of the root, represented in the binary system, is used. When extracting the cube root (also "column"), there are two differences from the decimal system. The first is that instead of 300 (the product of 3 and 100), the binary number 1100 is used (that is, the product of the binary equivalents of the numbers 3 and 4). The second difference is that instead of the number 30 (the product of 3 and 10), the binary number 110 is used (that is, the product of binary analogs numbers 3 and 2). To facilitate the selection of the next root digit (0 or 1), a number of standard values have been calculated, depending on the current root value. Assignments for independent work of students are offered.

Ditching Dewey and Developing a Love of Reading

This short professional paper takes a look at how I developed a love of reading by removing the Dewey Decimal system from the school library. I detail how I came to the decision, the process I followed and how the library is arranged and used today. There is also reference to other practices that have encouraged life-long readers, such as removal of all reading “incentives”, parent helpers, and ways to encourage families to use the library. The actual presentation of this paper is in the form of a slideshow. There will be talking, but every stage of the process and the ideas shared have pictures to go with them. Come and see it!

Storing information electrically in human skin

Human skin has been classified as a non-volatile memristor and it is shown that information can be stored within for at least three minutes. Here we investigate whether it is possible to store information up to 20 minutes. Furthermore, we investigate whether the information can be based on four different states, not just two (binary). We stored the information into the skin of the forehead of the test subjects under three different electrodes, which allows in principle for 64 different combinations (3 electrodes, 4 states) and one can think of numbers on the base of four. For this experiment, we decided on the numbers 1234 and 3024 (that correspond to numbers 27 and 50 in the decimal system). Writing of the different states was done by the application of DC voltage pulses that cause electro-osmosis in the sweat ducts (nonlinear electrical measurements). Based on our results, we were not able to distinguish between four different states. However, we can show that binary information storage in human skin is possible for up to 20 minutes.

Non-standard methods for converting numbers from one number system to another

The article describes a number of little-known methods for translating natural numbers from one number system to another. The first is a method for converting large numbers from the decimal system to the binary system, based on multiple divisions of a given number and all intermediate quotients by 64 (or another number equal to 2n ), followed by writing the last quotient and the resulting remainders in binary form. Then two methods of mutual translation of decimal and binary numbers are described, based on the so-called «Horner scheme». An optimal variant of converting numbers into the binary number system by the method of division by 2 is also given. In conclusion, a fragment of a manuscript from the beginning of the late 16th — early 17th centuries is published with translation into the binary system by the method of highlighting the maximum degree of number 2. Assignments for independent work of students are offered.

The Number Ten Reconsidered: Did the Pythagoreans Have an Account of the Dekad?

We critically reconsider an old hypothesis of the role of the dekad in Pythagorean philosophy. Unlike Zhmud, we claim that: 1) the dekad did play a role in Philolaus’ astronomical system, and 2) Aristotle did not project Plato’s theory of the ten eidetic numbers onto the Pythagoreans. We claim that the dekad, as the τέλειος ἀριθμός, should be understood in Philolaus’ philosophy as completeness and the basis of counting in Greek – as in most other languages – in a decimal system. Additionally, we argue that the number ten is not even a candidate for the τέλειος ἀριθμός in Plato’s philosophy. As a final result of our discussion, we compare and contrast Philolaus’, Plato’s, and Speusippus’ accounts of completeness in relation to numbers.

ETHNIC COMPOSITION OF THE POPULATION OF THE NORTHWESTERN DISTRICTS OF THE NOVGOROD LAND AT THE END OF THE 15 CENTURY

The article is devoted to the analysis of the ethnic composition of the population of the north-western districts of Novgorod land according to the toponymy and anthroponymy of the cadastres of the Vodskaya Pyatina 1499/1500. Orekhovsky district had several areas where the Baltic-Finnic oikonyms and anthroponyms were concentrated - these were Korboselsky district in the north of the Neva, Lopsky and Terebuzhsky districts in the southern Ladoga, as well as Dudorovsky and Izhora districts south of the Neva. The presence of Karelians is noted in the north of the Neva and in southern Ladoga. On the southern coast of Ladoga there were districts of the Ladoga district, where the Baltic-Finnish oikonymy is also found. Its percentage is declining to the east, towards the city of Ladoga. An analysis of the cadastres of the Koporsky, Yamsky and Novgorod districts allows us to conclude that the Baltic-Finnic onomastic tradition was concentrated primarily in the Toldozhsky and Kargalsky districts. This area is bordered by the valleys of the rivers Toldoga, Suma and Sista, the northwestern part of the Izhora plateau and the Soikinskiye hills. Slavic naming prevailed throughout the Vodskaya Pyatina. It turns out that in the villages where the Baltic-Finnish population lived, there was the so-called decimal system, the lowest governing layer of which was the decimal. As anthroponymy and oikonymy show, some of the decimals must have belonged to Votes and Izhora. In the middle of the 15 century Votes and Izhora had their own nobility, which is called «boyars». This nobility was incorporated into the socio-political system of Novgorod.

The “虚指Xuzhi ” of Number in Ancient China: Evidence from the Yijing

Number, especially the number system has been an important part of the Yijing text, which can help us probe into the myth of the Yijing. The Yijing languages treat numerical notion from ‘one’ to ‘ten’ very special, especially about the “虚指Xuzhi” (empty reference or implicit meaning) usage of ‘three’, ‘seven’, ‘nine’ and ‘ten’, etc. The numeral expressions and linguistic representations in the Yijing text indicate that the decimal system of numbers has been very popular at that time. From the analysis of the Yijing text, it can be seen that linguistic and cultural conceptualization of number exists and the usage of numbers at that time has reached “亿 yi 100 million”, which also indicates the strong numeral notions or ideas of the ancestors in ancient China. This paper mainly illustrates the “虚指Xuzhi” (empty reference or implicit meaning) of the original number in the Yijing by linguistic and cultural conceptualization of number, dealing with historical aspects of number usage.