[Music] we hello great tens and welcome to today's lesson what is ukian geometry have you ever wondered what the word geometry means in this lesson we join Eloise in a quick history lesson to discover what ukian geometry is all about we also see how we use it in the real world joining us today we have Sharon hi Sharon where are you and what are you doing hi everyone I'm here in my dad's study trying to find out where Matts comes from and who invented it and what have you found not much yet although I think I might need some help maybe I can help you I have found a few things take a look at this the world over every civilization throughout history has measured the heavens the Earth and achieved great Feats of construction and the mathematics used in those ancient times continues to be used today geometry the earliest known use of geometry was for measuring land so the word geometry comes from Geo meaning Earth and metry from the Greek word meaning measurement in 3000 BC the lands of Egypt and a part of Iraq known then as Babylonia and Assyria were flat and the large rivers flowing through these countries often flooded this meant that after every flood the people living on the river banks had to measure out the boundaries of their land this made them expert in the geometry of flat surfaces very quickly they learned how to create right angles use right angled triangles and they could calculate are years using simple multiplication the ancient Egyptians went on to use their knowledge of geometry to put up huge buildings that still stand today in those days concrete had not been discovered so they had to use their knowledge of geometry and their skills in stonework in order to build these huge buildings they did this by using huge hand cut blocks of rock and footing them together like a puzzle but it was their knowledge of triangles that led the Egyptians to develop a calculation for their most famous monument the pyramid their measurements were so accurate that these monuments have lasted for over 4,000 years and today we accept the pyramids as being masterpieces of straight line geometry wow buildings that have lasted over 4,000 years and they didn't even use cement that's pretty amazing but have you thought about what was happening in the rest of the world at the same time say somewhere like China well let's have a look during that same period the Chinese also suffered from floods as the yellow and yangi rivers often burst their Banks and their answer was either to build dams to hold the water or dig canals to let the water flow away then by 1,000 ad the Chinese had developed new skills they could build ships big enough to sail around the world although they never sailed them that far so what Maps do you reckon they use to build all these things geometry you got it let's carry on and see what else was going on in the world then if the Chinese had sailed across the Pacific Ocean to Central and South America they would have come across the people of the atic and Mayan civilizations like the ancient Egyptians they used geometry to build their own magnificent pyramids and temples but from about 600 BC Greek mathematicians went a step further they started to write books to explain and prove mathematics macal theories and many of these mathematical theories and proofs are still studied in schools around the world today Galileo galile an Italian astronomer and physicist who lived in the 17th century saw math as a tool and a language to describe the world he wrote The Great Book of nature lies ever open before our eyes and the true philosophy is written in it but we cannot read it unless we have first learned the language and the characters in which it is written it is written in the mathematical language and the characters of triangles circles and other geometric figures think about it people have been using geometry from as far back as 5,000 years ago now that's amazing and it's the same kind of geometry we learn in high school today as long as humans have lived in communities people have used maths to measure the land construct religious buildings and altars and calculate the positions of stars and planets in fact we still take our calendar and our measurements of time from the positions of the stars and planets today in schools we study three types of geometry ukian coordinate and transformation geometry so let's start with ukian geometry ukian geometry is named after the Greek mathematician uid he became famous by putting together a set of 13 books called elements in this collection uid recorded all the mathematical statements and proofs that the Greek mathematicians of his time had constructed then he arranged them into a formal system his Focus was on using logical thinking and deductive reasoning to make mathematical statements and then go on to prove them he called statements that had been proved to be true theorems but this isn't just history today much of our school geometry comes from uet's books the elements sometimes referred to as plain geometry ukian geometry focuses on points lines and shapes on flat surfaces or planes it is not concerned with what happens when the surface curves today we know the world is not flat but still people like Builders carpenters and surveyors Engineers Navigators and scientists use facts recorded in uet's elements to solve problems involving triangles circles quadrilaterals and other geometrical shapes but ukian geometry can be used even if you don't work directly with shapes because ucl's approach was based on logical reasoning it can be used to solve any problem we come across let's have a look at this situation and see how refill Weare uses reasoning to solve a problem it looks like rill we is having a problem m what's happened to my pen her first thought is to identify the problem the whole thing's come apart I can't write with this anymore it's useless now instead of just looking at the facts she is showing her disappointment how does she know the pen is useless let's see what happens when she tries again but maybe it can be fixed it won't screw together in the springs come out okay now she's identifying the facts let's see if she goes on to the next step but if I can find that spring and stick these two pieces together with glue it should work again now she's identifying what tools she needs to solve the problem the trouble is I don't know how the spring goes in I know I lost Gerard he can fix anything but but first I've got to find that spring and get a hold of some glue do you see how she's working through her problem step by step first she identified and made sure she fully understood the problem by identifying the facts then she made a plan to solve it after that she worked out what tools she's going to need in this case the tools are the spring and glue now she needs to carry out her plan Gerard my Pen's broken and I want it fixed I've got all the pieces and I have glue but I just can't figure out how to get the spring in place can you fix it for me let me have it go okay now that the plan is being carried out the final step is to check to see if it's solved the problem were you able to fix it good as new can I try it wow it's perfect you're a star do you see how the problem was solved no other school subject teaches us to approach a problem in this way we take it step by step using only facts that can be proved to be true there are no opinions no guesses no luck just plain logic ukian geometry teaches us to use reason a skill that is necessary if you want to be successful at anything in life seems a pretty easy skill to learn it is many people use this skill every day without even realizing they are doing it it makes an amazing difference to finally understand what ukian geometry is and to realize we all use its principles in our daily activities but how will we use ukian geometry in the classroom we will start by making our own conjectures a conjecture being a statement that has not yet been proved to be true then we'll take a closer look at some familiar shapes and make conjectures and generalizations about them and after that we'll practice proving or disproving these conjectures us using ukian coordinate and or transformation geometry this series will challenge you to go beyond memorizing someone else's definitions and facts it aims to help you develop your own body of geometry knowledge that you can prove to be true so get ready to do your own investigations thank you for joining us grade 10 you'll find tasks to practice these skills in the ukian geometry task video and on the mindset learn website keep practicing and revising in no time you CID be on top of your class [Music]