Examples of multiplication

Subject of occupations:
TRIGONOMETRIC FUNCTIONS IN A RECTANGLE
Subject of the previous lesson
Multiplication

Lesson 9

Examples of multiplication

Multiplication in space

At interaction of two one-dimensional spaces (in figure D is quantity of spacelike dimensions) the two dimensional space turns out. At addition to interaction of perpendicular measurement, the quantity of spacelike dimensions of result increases. It is necessary to understand any quantities participating in multiplication as spacelike dimensions. Multiplication of two one-dimensional lengths gives the two dimensional area, multiplication of the two dimensional area at one-dimensional length gives three-dimensional volume and so on. The possibility of receiving four-dimensional space as a result of multiplication of two two dimensional spaces is theoretically possible, but demands specification from the point of view of physical reality.

Examples of multiplication

Voltage is result of interaction of current intensity and resistance. If to consider current intensity not as one-dimensional quantity and as two dimensional (the area of current), then as a result of interaction with a resistance power will turn out. Units of measure of the specified quantities (Volts, Ampere, Ohms, Watts) are household (convenient in daily use), but demand mathematical representation for comprehension of an essence of the physical processes expressed by these units of measure. The system of physical quantities offered R.O. di Bartini can be considered as attempt of transition from household units of measure to mathematical. Interaction between quantities is carried out due to the processes studied in physics.

The arrangement of threads in the perpendicular direction allows to receive cloth. Interaction between threads is carried out at the expense of frictional force. If in the perpendicular directions to arrange reinforcing rod stock, then it is possible to receive a two dimensional reinforcing grid or a three-dimensional reinforcing framework. Interaction of separate rod stock in clusters is provided with electric welding or a knitting wire. Plywood is the fibers of a wood neveer located perpendicularly. Interaction is provided by pasting of separate layers of wood neveer.

At multiplication the quantity of goods on unit price, as a result turns out the cost of a consignment of goods (sum). It is an example of application of mathematical model of multiplication to the virtual units of measure. In this case physical interaction between goods and the price is absent.

Sexual reproduction it is possible to present in multiplication form. As a result of interaction of a male and a female there is a posterity which has genetic signs of two parents. Partial transfer of genetic signs from each of parents can be described by means of the linear angular functions.

For more precise reflection of reality in mathematician it is necessary to consider three stages of multiplication: beginning of multiplication, interaction process, end of multiplication. In electric circuits the switch is the device which operates interaction. Creation of cloth, plywood, a reinforcing grid is the beginning of interaction. Physical destruction of these objects is the end of interaction.

At the following lesson we will consider
Distinctions between multiplication and addition