字幕表 動画を再生する 英語字幕をプリント Uhh, parallel lines have so much in common... It's so sad they'll never meet :-( It's time to learn ge-om-etry NOW! Hey everyone, I'm your host Barby; After years of teaching you about border anomalies & trade export sectors & languages & cultures & landscape composition, I realise, I've been wasting my life. Seriously, it's time to finally think outside of the quadrilateral parallelogram & get you rational at this point & get you in shape for the trajectory this channel is heading in so without further ado... [Trumpet Sound] When It comes to the beginning, the earliest known case we have of documented geometric calculations comes from Ancient Egypt in which the Pharos would use rudimentary concepts and calculations to construct the pyramids with four triangular faces and square bases. Otherwise, many would attribute Greek mathematician Euclid as the father of geometry. Back then, a ton of people would come up to him for wisdom and he was all like "Yo check it! Any two points in space will totally make a straight line. Let's call this an axiom." Oh but he didn't stop there. Then he was like If two straight lines have equal space between them, they're parallel and hence will never intersect. If one or both of these lines are not at equal angles, they will eventually intersect. Then you can connect them and make a triangle. Oh and hey check it! If you take any point and a line segment, you can immediately create a circle by using it as a radius and other point as the center and circling it. Then, we can divide it into 360 degrees. And then all the people were like, "Why 360? That's such an arbitrary number isn't it?" Oh and then Euclid was like, "Na man, 360 is a perfect number because not only is it the number of days in our year, (with those pesky left over epagomenal five or six days.) but also its so wonderfully divisive. You can split 360 into equal groups of... 2, 3, 4, 5, 6. 8, 9, 10, 12, 15, 18 & 20! Dang!! That is a GOOD number! And from there - Euclid was taken -like- really seriously, as was the rest of the guys that were to follow him in the centuries to come. [Trumpet Sound] Now as mention in the last segment, it will depend on what exact shape or construct you wish to measure but basically you'll need points and lines. Today, we will cover triangles, quadrilaterals, and circles. Triangles can be tricky because they can come in six different forms based on the sides and angles. In regards to sides, scalene triangles have all different length sides, isosceles have two equal sides, & equilaterals have all three equal sides. Whereas with angles, an acute triangle has all angles less than 90 degrees, a right triangle has one 90 degree angle, and finally an obtuse angle which has one angle that is over 90 degrees. Keep in mind, you can have triangles with variables from both sides or categories. For example, an isosceles right triangle, or scalene obtuse triangle. However, keep in mind all equilateral triangles will be acute, however not all acute triangles necessarily have to be equilateral. Also keep in mind, isosceles triangles will always have complementary angles which means the two angles opposing the third one will always share the same value. Quadrilaterals are any shapes with four sides. They are generally classified into six different types: squares, rectangles, rhombuses, parallelograms, trapezoids, and irregular quadrilaterals. Squares share equal sides and are all right angles, rectangles have two longer sides but share right angles, the rhombus has equal sides but a set of different yet complementary angles, parallelogram is like the rectangle version of the rhombus with two sides longer, and the trapezoid has one parallel and one non-parallel set of sides in it's make-up. The irregular quadrilaterals do not follow any specific format however, some would say that the kite should be categorized as a quadrilateral as it has two sets of two different length sides. Otherwise, you can get an arrowhead, or this abomination nobody wants to invite to the party. Circles are the last and final variable we will include. These are strange because they have no points along the edge and technically only one side. In order to measure a circle though, they do maintain a central point for reference as well as an imaginary line that extends from the center to the edges to give the length of the radius and the diameter. This line, although imaginary to the construct of a circle, is crucial because without it circles wouldn't exist. You need the diameter for π. What is π? Basically, the ratio of the circumference to the diameter. A rough but slightly inaccurate approximation would be 22/7. Technically, π is an irrational number because the digits go on and on forever to the point that π has no recognizable value. An irrational technically unrecognizable number for all our curvature calculations. Speaking of which. [Trumpet Sound] Geometry is actually in a lot of ways like cooking. Every shape ever made has a recipe. To make the perfect one, you need to know which components get mixed into together. Let's start with triangles. In order to find the area of a triangle, you multiply half times the base times the height. Now all quadrilaterals are a little different. To find the area of a square, you simply just square the sides. For rectangle, you do the length times width. For parallelogram, you do the base times the height. And for trapezoid, you multiply the height by both bases added together divided by two. Now, circles are a bit stranger. As mentioned before, you need to have π. So the area of a circle is π R squared in which you square the radius. The circumference of a circle, keep in mind, is 2π R. And that's about it. In conclusion, this world might be made up of majestic mountains and vibrant cultures and people groups but in reality, we all also live in a world of calculations and numbers that direct our very existence without us even knowing it. Thank you for watching. This episode was brought to you by the government of Bandiaterra. Woo Hoo!