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Math III Videos 103 videos
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Constructions 1889 Views
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Description:
No hard hat needed here–we're talking about mathematical constructions. If you're using a straight edge, a compass, and a pencil, you're working with a construction.
Transcript
- 00:04
constructions in geometry a la shmoop some people are happy being famous even [Woman walking down red carpet]
- 00:10
with all the bad press they get some people like helping others and making a
- 00:14
difference in the world regardless of how much money they earn and some people
- 00:18
find true inner peace just by sitting on top of a construction scaffolding with [Man on top of crane]
- 00:22
hard hats and day-old turkey sandwich of course construction isn't all about
Full Transcript
- 00:26
hammering up drywall and playing with power tools it's also about being
- 00:30
creative in geometry a construction is a drawing that you make using only a
- 00:35
straightedge a compass and a pencil a straightedge is anything you can use to
- 00:41
make a straight line like a ruler or the back of your geometry textbook or a
- 00:44
two-by-four a compass might point north if you're venturing through the Amazon [Person checks compass in Amazon rainforest]
- 00:49
but in geometry we're talking about this thing which preserves distance and draws
- 00:54
a perfect circle make sure to pack the right compass next time you're going on
- 00:58
safari we use a pencil because well mistakes happen and whiteout is really
- 01:02
expensive using only these three tools we can
- 01:05
construct practically anything a perpendicular bisector a congruent angle
- 01:10
an equilateral triangle or parallel lines let's try a relatively simple
- 01:17
construction how do we construct an angle congruent to this given angle [Angle appears]
- 01:22
we'll start by drawing array which will be one of the sides of our new angle now
- 01:28
we can use our compass to mark an arc length within the given angle with the
- 01:33
centre at the endpoint of the angle without changing the measurement of the
- 01:37
compass let's draw an identical arc on our ray we adjust our compass to be the
- 01:42
distance between the intersections between the arc and the sides of the [Person uses compass to mark an arc on the angle]
- 01:47
given angle if we take this distance and apply it to the intersection between the
- 01:52
arc and the ray we can draw a small arc that intersects with the
- 01:56
two points are enough to draw another ray from the endpoint of the angle
- 02:01
through the point where the two arcs intersect and there you have it a
- 02:05
congruent angle constructed using only a pencil a straightedge and a compass it's [Construction worker holding a ruler, pencil and compass]
- 02:10
no Eiffel Tower but it'll do
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