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  • 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!

Uhh, parallel lines have so much in common...

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B1 中級

幾何学ナウ! (Geometry Now!)

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    林宜悉 に公開 2021 年 01 月 14 日
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