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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

• [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.

• 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.

• 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.

• 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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# 幾何学ナウ! (Geometry Now!)

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林宜悉 に公開 2021 年 01 月 14 日