Know some special words in mathematics like “What is L’ Hospital‘s rule and Pappu’s theorems”?

What is amplitude?

The amplitude is the maximum value of a varying quantity from its mean or base value. In the case of a simple harmonic motion wave or vibration – it is half the harmonic motion wave vibration is half the maximum peak-to-peak value.

What is ambiguous?

Having more than one possible meaning, value or solution. For example, if we are given two sides and one angle other than the included angle of a triangle, it gives rise to an ambiguous case in finding the other side and angles of the triangle. One solution is an acute-angled triangle and the other is an obtuse-angled triangle.

What is the Base period?

The period used as a standard for comparison for some variables, for instance, consumer prices 100 is usually taken as the index number for the variable in the base period, so that an index of 150 for a given period indicates that prices then were one and a half times those of the base period.

What is Birkhoff’s theorem?

Birkhoff’s theory is every matrix can be expressed as a convex combination of permutation matrices.

What is bisector?

A bisector means a straight line or a plane that divides a line or a plane, or an angle into two equal parts. The equation of the line bisecting a given angle is obtained by equating the perpendicular distances from a variable point to each of the lines forming the angle. The equations of the planes bisecting the angle between two given planes are obtained by equating the perpendicular distances from the variable point from the two given planes first giving these distances like signs and then unlike signs.

What is Bolzano’s theorem?

Bolzano’s theorem is a single real-valued function f(x) of a real variable x, is zero for at least one value of x on [a,b] if it is continuous a [a,b] and f(a) and f(b) have opposites signs.

What is Central projection?

Central projection is a geometrical transformation in which a straight line from a point to each point in the figure is continued to the point at which it passes through a second plane. These points form the images of the original figure. 

When a photographic image is created from a film using an enlarger, this is the kind of projection that takes place. The light source is at the centre of the projection, the light rays are the straight lines, the film is the first plane, and the screen or point is the second. In this case, the two planes are usually parallel, but this is not always so in central projection.

What is Leibnitz’s theorem?

This is a rule for finding the n^th derivative of the product of two functions. It is expressed as a series of (n+1) terms involving successive differentials of separate functions and binomial coefficients.

What is L’ Hospital‘s rule?

This is a mathematical rule which permits the evaluations of the limit of an indeterminate quotient of functions as the quotient of the limits of their derivates.

For example

X→0 cos x/1 =1

What are Pappu’s theorems?

Pappu’s theorems are two theorems concerning the rotation of a curve or a plane shape about a line that lies in the same plane. The first theorem states that the surface area generated by a curve revolving about a line that does not cross it is equal to the length of the curve times the circumference of the circle traced out by its centroid. The second theorem states that the volume of a solid of revolution generated by a plane area that rotates about a line not crossing it is equal to the area times the circumference of the circle traced out by the centroid of the area.