ShmoopTube

Where Monty Python meets your 10th grade teacher.

Search Thousands of Shmoop Videos

Formal Proofs 1856 Views


Share It!


Description:

Formal proofs present the oh-so-mathematical evidence in two columns: one for the statement they are claiming is true, and the other for the reasoning behind them.

Language:
English Language

Transcript

00:04

Formal Proofs, a la Shmoop.

00:09

Dear Sir or Madam, you are cordially invited to attend the Formal Proof,

00:15

a black tie event exclusively for geometers of the highest esteem.

00:20

Upon arrival, please form two columns and show this invitation at the door for admittance.

00:26

A-list members from all circles of the geometric world will be in attendance.

00:30

So please wear your best surface area, and enjoy live music,

00:35

complimentary cheesecake, and a night to remember.

00:38

Proofs are all about showing evidence for why something is true,

00:42

kind of like the detectives on your favorite crime show.

00:45

Formal proofs take this a step further.

00:48

They present the evidence in two columns:

00:51

one for the statement they're claiming is true

00:54

and the other for the reasoning behind them.

00:57

Usually these reasons take the form of definitions, theorems, postulates, or given information.

01:04

They lead us step-by-step from the hypothesis to the conclusion, like fancy tour guides.

01:11

So if A equals B and B equals C, can we prove that A equals C using a formal proof?

01:20

Well, let's give it a shot.

01:21

First, we'll make two columns: tone for statements, one for reasons.

01:24

We'll start with what we know.

01:26

We can say that A equals B, because that's given to us.

01:30

Same goes for B equalling C - given.

01:34

We want to prove that A equals C,

01:37

so we can use the transitive property of equality. That's all it takes.

01:43

We've proved what we wanted to prove using a formal proof.

01:46

Once you learn more definitions and theorems,

01:48

you'll be able to write longer, more complicated proofs. Don't look too excited.

01:52

If we can write formal proofs, we're certainly geometers of the highest esteem.

01:56

So let's head to that ball and have ourselves a big old hunk of cheesecakeā€¦

02:00

or five.

Up Next

Surface Area of Cylinders
14740 Views

Haven't you always wondered how much cardboard it takes to encase a trunk warmer for your pet elephant?

Related Videos

Perimeter of Irregular Shapes
4864 Views

Want to figure out the area and perimeter of irregular shapes? Break them down into regular shapes. For example, a flower can be broken down into s...

Introduction to 3D Geometry
55502 Views

It's one thing when all those shapes are sitting flat on the page. But when they start popping out and invading our personal space bubble, we get a...

An Introduction to 3D Geometry
812 Views

Does thinking about 3D Geometry get you bent out of shape? Never fear! Watch this video and figure out some fun new shapes to bend back into. We're...

ACT Math 3.5 Plane Geometry
394 Views

ACT Math: Plane Geometry Drill 3, Problem 5. How long would it take for the wheel to make two rotations?