The Ancient Greek scientist Pythagoras lived in the sixth century B.C. People use its many opening still. One of such useful things which are thought up by the great mathematician and the philosopher – Pythagoras's table.
It is required to you
- - ruler;
- - pencil;
- - sheet of paper;
- - computer with the editor of Microsoft Word.
Instruction
1. Pythagoras's table is the multiplication table represented in the form of a square. This square is divided into lines and columns. In the top line and an extreme left column natural numbers in that order in which they go register. The work of the corresponding numbers is written in the cell located on crossing of a line and column.
2. It is possible to draw Pythagoras's table on the sheet of paper. Draw a square. Divide it on a vertical and a horizontal into identical quantity of parts. For example, it is possible to give marks through each centimeter. Having connected the marks located the friend opposite to the friend, you receive the big square consisting of a set of small.
3. In the top line, having receded 1 section at the left, write a number of natural numbers. In an extreme left column, having passed the top section, also write a number of natural numbers. In the section which is on crossing of the first line and the first column write the work of numbers by which this line and a column are designated. In this case it is units, that is it is necessary to put number 1. On crossing of the first line and the second column put number 2, on crossing of the same line and the third column – number 3. Continue to fill out the table, multiplying each of the numbers standing in columns by 1.
4. Fill the second line. Each of the numbers standing in columns needs to be multiplied by 2. Thus, in the first section there will be number 2, in the second – 4, in the third – 6, etc. Fill all second line, and then and all others, multiplying the numbers designating each column by 3, 4, 5 and other numbers of a natural row. Such table can help out very much if it is necessary to solve urgently an example on multiplication, and the calculator near at hand will not appear. To find the work of two natural numbers, it is rather simple to find the corresponding cell.
5. Pythagoras's table can be made also on the computer. However, in the usual Microsoft Word program or similar the plate will hardly turn out square, but it is not so important. Find the Table tab in the top menu, and in it – "to Insert". Insert the table with identical quantity of lines and columns. If desired it can be made square, having set the cell sizes.
6. Fill out the table just as in the first way, that is in the top line and a column extreme at the left gather one after another natural numbers. Fill other sections with works of the corresponding numbers. The table is ready.