Understanding Linear Measurement in Maths

Linear measurement is the measurement of the distance between the two points or objects, or it can also be defined as the gap between the leftmost end and the rightmost end. Linear measure refers to measurements that are directly proportional to the distance traveled along the axis of the measurement. For example, the length of your dining table, the height of a chair, the distance from your hall to the kitchen,  all these come under the examples of linear measurement.

Linear measurement is achieved by various instruments, depending on the type of instrument used for measurement. It can be divided into a direct measurement method, an optical measurement method, and an electronic measurement method.

Direct Measurement Method

It is obtained by using some simple measurement equipment. The direct measurement methods are widely used in the fieldwork measured using a chain or chape. All the instruments used for the chaining process in the direct method are chains,  tapes, arrows, ranging rods and offset rods, pegs, and the plumb-bob.

Optical Measurement Method

In the optical measurement method, observations are taken through the telescope, and calculations are done for distance as in tachometer or triangulation. The tachometer is a type of surveying method used to determine the horizontal distance from to and evolution of a point.

Electromagnetic Methods 

In electromagnetic methods, the distances are measured with the help of instruments that are based on propagation, reflection and subsequent reception of either radio or light waves. Some of the instruments used in the electromagnetic method are Geodimeter, Tellurometer, Decca Navigator, etc. All the methods were found due to the problems faced in convention taping distance measurement.

Basic Tools of Linear Measurements

Some of the basic tools used for linear measurements are given below.

Ruler – The standard rulers generally measure 15 and 30 cm with markings in mm, cm on top and inches on the bottom, Some of the 15 cm rulers you would have used in the schools.

The markings on the tape and ruler are in the metric and customary system and the next section lists the different units of measurement for length and height. Using measuring instruments like a ruler and a scale, it would be very easy to measure the object in the surroundings like a pencil, shoe, remote, car, spoon, and toy.

Units of Linear Measurement

The measurements of length can be measured by using a linear measurement unit. Linear measurement units have a reference line or axis. A measurement unit can move along this line from the reference point. The distance moved over the reference point is the length of the measurement unit. The common system of  linear measurement units are given below:

U.S. Customary Units for Linear Measurement

The US Customary Units for linear measurement (also called custom unit or USU) is a set of units of linear measure with values derived from the United States customary system of measure.  They are used for the measurement of linear quantities for both metric and imperial (U.S. customary) systems of measure. They are Inches (in), Foot (ft), Yards(yd),   Miles (mile).

Metric Units for Linear Measurement

In Metric Units, the distance between any two points is measured in metres (m). The distance between points in Metric Units is calculated by subtracting their starting point from their ending point and multiplying that result by the length of a unit. The length of a linear unit varies, depending on which linear unit is being used. These metric units are Millimetres (mm),  Centimetres (cm), Metres (m), Kilometres (km).

Various Standards of Linear Measurement

According to the linear dimension measurement, there are three important standards used for the linear measurement are:

• Imperial Standard Yard - According to this standard 1 yard = 11 feet and 1 foot = 12 inches.

• International Prototype Metre - According to this standard 1 m = 100 cm and 100 cm = 1000 metre.

• Wavelength Standard - According to this standard 1m = 1650763.73 light waves of a red-orange line of Krypton-86.

The different methods used for doing linear centimetre measurements are the line standard method of measurement, end standard method of measurement, line and end standard method of measurement.

Applications of the Linear Measurement

Measuring is the quantitative analysis and it is the primary step for the measurement of distance. Some of the measurable quantities include such as length, breadth, and height, the knowledge of physical and linear dimensions of objects is used in learning geometry, drawing scalable maps, architecture, and estimating unknown quantities for shapes with the help of formulas.

Fun Facts

• In the early days, the basis of acceptable measurement was the length of the body.

• According to the order of King Edward II of England, one inch is equal to 3 grains of barley from end to end.

• The feet of the Cossutius statue in Rome measured 30.49 cm, which is the measure of 1 foot.

• The Romans used copper measuring rods in the 16th century for construction and construction purposes.