Nicholas Albrecht presents:

My math presentation

of parallel and

perpendicular lines…

And mathiness and history

These were from some ancient Roman or Greek guy. His name was Euclid (for parallel). Though there was much talk about lines that crossed in a 90 degree way, the first time it was used in math was by a French philosopher named Cartesian.

They have been used by many unsmart people (who couldn’t figure out how to make something like it without it… without math) to build many things like buildings or streets or stovepipe hats in the early, undeveloped times of the world.

Streets sometimes also have perpendicular lines, buildings to, but not really stovepipe hats.

First thing of importance: history of parallel and perpendicular lines

These lines are on the same plane and NEVER intersect.

They have the same slope

They go on forever because they are lines, so by definition they are infinite, so if they never intersect, they are somewhat unusual (though with how often we are using them, I am not so sure)

They are all over the place.

Parallel lines:

These are lines that intersect at one and only one place

Lines are generally straight, and go on forever so lines can only intersect something once.

The lines form exact right angles.

They are also LINES, so they go on forever, just the ONE place where they intersect forms a right angle.

Perpendicular lines:

Be prepared, those who proceed may not return from the land of the math.

Smore history

The ancient Romans used perpendicular a lot in there architecture, they never used it in math, the Greeks didn’t either. Cartesian was a French Philosopher who first used these lines. Cartesian was actually the French version of the Latinized name people gave him, his real name was Rene Descartes. The pure Latin name was Cartesius. He was one of the big mathematicians, like Euclid, or Aristotle, though he was French and not Greek, Roman, or Chinese. He is very famous for the Cartesian Coordinate system. He was born on March 31, 1596, and died on February 11, 1650, he came into the world much later than most mathematicians, and Euclid who invented Geometry. Cartesian was a guy who really made things easier for the mathematicians in a place where they knew nothing for thousands of years. Perpendicular lines were used so often by so many cultures during and after the Fall of the Roman Empire, it is amazing that perpendicular lines had not been “discovered” before then, but it makes the idea of Cartesian being a real genius obvious.

The complete history of these lines VOL1: perpendicular lines

This was made by Euclid, an ancient Greek Philosopher. He was alive around the time of 300 BC. He invented the core idea of Geometry and most of the ideas and math that goes into it. Parallel lines are one of the things that he thought of and made an important part of Geometry. He was thinking of things that never intersect each other, then thought of them as lines that are infinite, and called them parallel. Thus parallel lines were born. Later came the equations and transversal lines and the actual math that goes with it. Most of that Euclid also came up with. It was Descartes who thought of perpendicular lines which are the “opposite” of parallel line, so obviously they are still a major part of parallel lines. He is an example of someone who helped the evolution of Geometry without Euclid doing it.

The complete history of these lines VOL2: parallel lines

There are a lot of things in our world that can be called parallel, but they are only called that because of an old Greek guy who came up with the idea for math. Though there are many things in our world that have the mathematical parallel lines in them, that may have happened accidentally. People might have designed streets by only thinking about making it straight, not about parallel lines, depending on when it happened, they may not have even known about parallel lines. Of course, there were wagons that would make tracks that turned into a road, that happened to be parallel, but wagons were just made to go straight, not make lines.

Parallel lines, continued:

Boxes you get in the mail usually are designed with perpendicular lines, they sometimes don’t look that way when they come, they have been beet and have large dents or rips in them after there journey to you. It is a little harder to think of perpendicular lines in our society, humans seem to like things that “go with the flow”, rather than intersect and point at a new direction, like perpendicular lines do to each other even though they form an orderly shape with a right angle.

Perpendicular lines continued

This is currently the tallest man made building on this planet, you can see almostNo perpendicular lines on it, instead youSee lots of parallel lines.

The Taipei 101 was once the tallest building, but not anymore. It is a rare type of building.It has a lot of perpendicular lines, though they Were not supposed to be that way.

The Apple symbol HAS NO PARALLEL LINES!!!!!

PC logo does

Android logo does.

A mathematical reason why Apple stinks!!!

…?These are obviously some more examples of parallel lines that probably happened because some guy wanted it to look cool (or for the thing it was representingTo work…)

Maybe the apple went bad…

Mwhahahah!!!! Is this presentation 38-40 min yet?

Intermission: half time showBig marching band and some random singer comes to the field and sings some horrible song (with a few exceptions)

Now is this presentation 38-40 min?

No!?!?!?!?!?!?! D***!

These lines cut parallel lines usually at odd angles, but sometimes form two or more sets of perpendicular lines. Transversal lines are still lines so they are straight and infinite, they only intersect one line one time. As far as we have learned, there cannot be a transversal of perpendicular lines, there can be a line intersecting both, but not perpendicular.

Transversal lines

statement reason<1 and <3 and vertical

Given

<1 and <2 form a linear pair<2 and <3 form a linear pair

Definition of linear pair

<1 and <2 are supplementary<2 and <3 form a linear pair

Postulate: if two angles form a linear pair, then they are supplementary

M<1+m<2=180M<2+m<3=180

Definition of supplementary angles

M<1=m<3 Algebra<1 is congruent to <3 Definition of congruent

angles

Vertical angles are congruent proof- it only looks pretty because it was copied from word, and it automatically did that

Corresponding- 6 and 1

Alternate exterior- K and H, 6 and 3

Consecutive interior- 1 and 4

Alternate interior- 2 and4, 1 and 5

Similarities of angles

1 2

3

4 56

Congruent corresponding angles

Congruent alternate exterior angles

Congruent alternate interior angles

Supplementary consecutive interior angles.

Some reasons you can use for proving lines parallel, remember these for the test!

Distance formula: D=

Equation of a line: y=mx+b

Formula for a slope:

Point slope form:

Some important equations

Civil Engineer

these engineers design buildings and roads and bridges. Though nowadays roads are designed with parallel AND perpendicular lines purposely, the engineers are constrained by that in their unique bridge designs. Buildings sometimes have whacky designs, but on the inside, the hallways are normally made with parallel walls, and intersecting halls are often perpendicular. You cannot have a road or a set of train tracks that have both sides intersecting somewhere, because with a train, it would simply jump off the rails and crash and explode! (would be fun to watch in a movie, but not in real like… sometimes)

Mechanical engineer

These build and design tools and machines. Many machines need to be able to make things that are parallel, and not skew things all up. Computer parts for example, they must be very precise, if one thing is just slightly out of place, it wont work right (or left because it wont work at all). A lot of parts for almost anything these days require parallel lines (its not the 80’s anymore, we are NOT building houses like the Jetsons would have. Mechanical engineers don’t design the 80’s houses, but they design the tools to make them so the civil engineers can have fun designing weird stuff.). The way most people think, you would need mathematical parallel lines and perpendicular lines in your rack of knowledge, otherwise, you probably would have a hard time getting a job in any of these fields.

Two careers that require these kinds of lines

I have mentioned this before, but here are some more examples.

I’m sorry David, but they are even in Star Wars. And knowing Star Wars, they probably were thinking of math at that time. However, there are very few; which is a mathematical reason why they don’t work.

Parallel lines really are everywhere

They are in many stories, historical, fantasy, and SCI-FI alike. Even horror stories sometimes do.Even the stories them selves as in the book they are told in.

Google (and Google Chrome)

Bing

Toshiba

Acer

…math

Logitech

Fire Fox

Unfortunately, the math book

THE WORLD!

No help from Apple

And weather you like it or not, this was thorough and beneficial

Prepare for a study guide…

Credits: