Euclid's Parallel Postulate

There are many conspiracy theories, but none of them outweigh that of the $300$ B.C. conspiracy of Euclid's Parallel Postulate. How you may ask? Well it is the year $2019$ and only one of Euclid's Presumptuous Postulates have been solved.

Quick Maths

Are we living in a simulation? With English just being a version of Simlish?

Here, we are using the superior align $$\begin{align} 1 &= 2\\ 2 &= 3\\ 3 &= 4\\ 4 &= 5\\ 5 &= 6\\ 534234 &= 342355\\ \end{align}$$

Here, we are using the inferior double dollar signs $$1 = 2$$ $$2 = 3$$ $$3 =4$$ $$4 = 5$$ $$5 = 6$$ $$53243 = 524234$$

taken from Euclid's Elements, Book 1

The famous Parallel Postulate, or Postulate 5:

That, if a straight line falling on two straight lines makes the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which are the angles less than the two right angles

What could this possibly mean? Let's take it apart.

If a straight line falling on two straight lines- so we have three lines

makes the interior angles on the same side less than two right angles- so the interior angles formed sum to less than 180 degrees

then the postulate says that those lines will intersect.

This seems obvious (that's why it's a postulate): Because if the sum of the angles is less than 180, then let's say that angle equals $x$. Then if we have another angle that's $180-x$, the three angles sum to 180, and they form a triangle!

If the lines form a triangle, they aren't parallel.

If the sum of the angles were greater than 180, the sum of the angles on the other side would be less than 180, so they would intersect.

In fact, the parallel postulate is equivalent to the fact that the sum of the angles in a triangle is 180 degrees.

Another equivalent statement is that "Given a line l and a point P not on that line, exactly one line goes through P parallel to l"

(I know this was very wordy for a geometry diagram. The parallel postulate was so controversial for this reason)

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Sphinoglipid

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Eucy and His Parallel Posse

Title

euclid was a pretty cool dude. He was once known for saying,

"$4=5$ $$123=456$$ swag swag golly gosh wohhhooot"

Truly wise words indeed. But that's not all! Want to know more?

Press continue to keep learning

Do you ever wonder about Euclid's Parallel Postulate? Well, look no further! Here is the solution, just for you!

a portrait of the author as a young man (Colorized, 1899)

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Jk jk

$\text{Unless}\dots$

$$\begin{align} 3x&=4\\ x&=\frac43 \end{align}$$ $$\begin{array}{c|c|c} 1&2&3\\ \hline 4&5&6 \end{array}$$ $${\color{Red}{4x}}+3\\ {\color{red}{4x}}+3$$

Hi

• hi 1
• hi 2
• hi 3

Yes

1. no
2. unless
3. jk

$\sqrt{3}$

$\sqrt[3]{3}$

$$\sqrt[\begin{array}{c} 1&2&3\\ 4&5&6 \end{array}]{\begin{align} 3x&=6\\ x&=2 \end{align}}$$

$\lim{\infty}$

Hi $\phantom{42342424}$ bye

$4x\quad4\\ 4x\,\,3$

test test $test$