Geometry comes from the Greek geo ("earth") and metron ("measurement"). The Greek mathematician Euclid, often referred to as the "Father of Geometry", was the first to describe a formal system for geometry in his textbook the ‘Elements’ in the 3rd century BC. Euclid’s ‘Elements’ was the main text for teaching mathematics from the time of its publication until the early 20th century!
The Greek philosopher Thales used geometry to solve problems such as calculating the height of pyramids and the distance of ships from the shore in the 6th century BC. However Indian and Babylonian mathematicians had also known of these theories prior to Thales.
French philosopher, mathematician, and writer René Descartes, 1596–1650 or (latinized: Renatus Cartesius), is credited as the father of analytical geometry, the bridge between algebra and geometry. The Cartesian coordinate system allowing reference to a point in space using a set of numbers was named after him.
Geometry is used in all fields of engineering.
Photo: A European and an Arab practicing geometry in the 15th century. Public domain image from the Wikimedia Commons
Geometry is part of the national engineering unit MEM30012A Apply mathematical techniques in a manufacturing engineering or related environment. More details on unit content from training.gov.au
Required skill: use two dimensional geometry to solve practical problems that involve concepts like perimeter and area, and convert between Cartesian and Polar coordinates, respectively. Solve three dimensional problems involving volume and surface area.
There are no prerequisites required for this module. However, to complete the lessons and quiz below you should have an understanding of arithmetic.
Civil Engineers use geometry for survey calculations to find the location of roads, railways and building sites from known reference points, watch this example video.
Chemical Engineers use geometry to calculate the volume of tanks for the design of chemical manufacturing plants. Watch the following video from the LearnChemE youtube channel for an example on how engineers use geometry.
Electrical Engineers use geometry to calculate the phase relationships of AC electrical current and voltage.
Manufacturing or Industrial Engineers use geometry to plan the layout of manufacturing plants, see this example video.
Mechanical and Structural Engineers use geometry to calculate the mass of machines and structures, see this example calculation video.
Please complete the following lessons.
Angles, degrees, and radians.
Maths is fun lesson on Degrees Angles with a 9 question quiz at the bottom of the page
Khan Academy angle basics series of video lectures - there are 6 short videos in this series and 3 practice sections (starred)
Two dimensional figures perimeter and area.
Maths is fun lesson on Plane Geometry
Khan Academy basic geometry series of video lectures - there are 7 short videos and 2 practice sections (starred)
Three dimensional figures volume and surface area.
Maths is fun lesson on Solid Geometry
Khan Academy solid geometry series of video lectures - there are 5 short videos and 3 practice sections (starred)
Cartesian coordinate system, and the equation of a straight line.
Maths is fun lesson on Cartesian Coordinates with a 10 question quiz at the bottom of the page
Maths is fun lesson on Equation of a Straight Line with a 10 question quiz at the bottom of the page
Khan Academy Descartes and Cartesian coordinates series of video lectures - there are 9 short videos and 5 practice sections (starred)
Khan Academy graphing linear equations series of video lectures - there are 8 short videos and 3 practice sections (starred)
All Khan Academy content is available for free at http://www.khanacademy.org/
Angles, degrees and radians
The Tesla model S electric car has a motor power output of 185 Kilowatts (kW) and a maximum Torque output of 270 Newton metres (Nm). From the equation below, what would be the motor speed in revolutions per minute (rpm) at maximum power and torque?
Given, P= Tω where P = Power (Watts) 1 kW=1000 W, ω= Angular velocity (radians/sec) and T = Torque (Newton metres).
From the power equation, angular velocity 
rad/sec. To convert to revolutions per minute we apply that 1 revolution=360° =2π radians. Hence, 
revs/sec. To find the motor speed in revs/minute we apply the fact that there are 60 seconds in each minute leading to ω = 109 x 60 = 6543 revs/min.
Two dimensional figures perimeter and area
A domestic solar power installation requires 2.5 kW of solar capacity made up of ten 250 W panels with dimensions of 1027 mm x 1695 mm (Tindo Solar Karra-250), what would be the minimum roof area to install this system, assuming no gaps between panels?
Area 1 panel = 1027 x 1695= 1740765mm2 or 1.74m2
Total area required = 10 x 1740765=17407650 mm2 = 17.4m2
If a mounting frame was to be built around the perimeter of the panels, what length of steel would be required for the frame?
Assume 2 rows of 5 panels hence total length l=1027 x 5=5135mm, width w = 1695 x 2 = 3390mm hence perimeter = 5135 x 2 + 3390 x 2=17050mm or 17.05m of steel required.
Three dimensional figures volume and surface area
Find the energy required to heat a new swimming pool with dimensions of 25 x 8 x 2 m by 5°C above the ambient temperature. Given the volumetric heat capacity of water at 25°C = 4.179 J/[cm3 K]. (Where K=Kelvin the unit of absolute temperature having the same magnitude as Celsius)
Hence, the heat energy E required in Joules (J) is given by E = 4.179 x V x ΔT where ΔT = 5°C
We need to calculate the water volume V in cm3 V=l x w x d and 1m=100cm hence V=2500 x 800 x 200= 400,000,000 cm3 therefore
If gas costs 4.1c/MJ how much does it cost to use gas to heat our pool by 5°C assuming a 100% efficient heating system?
Cost =8,358 x 4.1=$342.67
Practice exercises:
1. The performance version of the Tesla electric car has a maximum power output of 310 kW and a maximum torque of 600 Nm. Given the power equation above, what would be the motor speed at maximum power and torque in revolutions per minute or rpm?
2. A domestic solar power installation requires 3 kW of solar capacity made up of 250 W panels with dimensions of 1027 mm x 1695 mm (Tindo Solar Karra-250). What would be the minimum roof area required to install this system?
3. To install a swimming pool a hole must be excavated 20 m long x 7 m wide x 2.5 m deep. Calculate the volume of soil that must be removed from the site?
4. Calculate the surface area required for a thermal blanket to cover the water surface of the pool in Q3.
Click here to check your answers
Math.com Free math lessons and homework help.
Interactive Maths Geometry exercises with solutions
SOS Mathematics exercises with solutions
Worked geometry examples and free tutoring at Algebra.com
When you have completed the lessons, verify your knowledge with this multiple choice Geometry Quiz
PLEASE NOTE:
Trigonometry comes from the Greek trigōnon ("triangle") and metron ("measurement"). The Greek mathematicians Euclid and Archimedes in the 3rd century BC were the first to prove trigonometric formulas geometrically.
Throughout history carpenters and masons have known of a quick way to confirm a true ‘right angle’. It is based on the most widely known Pythagorean triple (3, 4, 5) or the ‘Rule of 3-4-5’. From the right angle, run a straight line along one side exactly three units in length, and along the second side exactly four units in length, this will create the third side, or hypotenuse of exactly 5 units in length. The geometric law behind this is the Pythagorean Theorem, e.g., for the triangle to the left
c2 = a2 + b2 or c =
Trigonometry is used in all fields of engineering.
Photo: Parts of a right angle triangle, also known as a 30-60-90 triangle after the internal angles.
Public domain image from the Wikimedia Commons
Knowledge of statistics is like a knowledge of foreign languages or of algebra; it may prove of use at any time under any circumstances. - Sir Arthur Lyon Bowley
Statistics and probability are used in all fields of engineering.
Statistical methods are used to analyse data collected from testing, experiments and from the environment. Probability methods are used to predict the likelihood and risks of failure, likelihood of events such as errors, accidents and cyclones. This analysis allows design changes to keep failures to an acceptable level for the application at hand. Watch Rebecca’s Reliability Engineer career story.
Statistics are also concerned with gaining information about a population from a small sample of that population. For example, in product design engineers may need to know the size of the average, largest or smallest person using a product. This information is usually available in handbooks based on measurements taken from a small group (or sample) of a large group of people.
Photo: Plot of normal distribution curve each coloured band has a width of one standard deviation.
Image licensed under the Creative Commons Attribution 2.5 Generic from Wikipedia
Algebra is a type of mathematical shorthand consisting of symbols and signs. These algebraic symbols represent numbers that are not known, ‘unknowns’ or represent unspecified numbers or ‘parameters’. This allows us to state relationships or prove properties no matter what numbers are involved, for example, the quadratic equation has parameters a, b and c, and an unknown variable x.
"Algebra" is derived from the Arabic al-jabr or “restoration”, one of the two operations used by Abū ʿAbdallāh Muḥammad ibn Mūsā al-Khwārizmī to solve quadratic equations. Al-Khwārizmī was a Persian mathematician, astronomer and geographer during the Abbasid Empire, and a scholar in the House of Wisdom in Baghdad. His work was based on older Indian or Greek sources.
Algebra is used in all fields of engineering.
Photo: Plimpton 322, Babylonian tablet showing a positional number system that greatly aided the solving of rhetorical algebraic equations, the early origin of Algebra. Public domain image from the Wikimedia Commons