Tangent & Radius are Perpendicular (Proof by Contradiction)

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I can feel the love you have for learning and teaching maths. Keep it up sir

Mech.Masters

Man! He drew a STRAIT line from O to x intersecting the circle at b without a ruler! That's talent!

mikedebell

Just look how straight that Ox line is with no ruler

angelopinheiro

Finally a math teacher that doesn’t start a lesson by saying: “Ok, this is going to be boring...”

No shit math ain’t boring

tristanmoller

I got my degree in math about forty years ago and I love this channel. He goes over a lot of stuff that I took for granted for decades and I sit here and go "Wow! I never knew that." For example, I've known about sines and cosines since 10th grade trig BUT no one ever explained that cosine is shorthand for the complement of sine. Also, I now see the relationship between sine and sinuous (I'm fascinated by words and their origins.).

goldwinger

I like that if BX is negative, you can imagine X is inside the circle. Therefore the line PQ cuts the circle in two places, so it isn't a tangent... which is a contradiction because we defined it as such in the set up.

InTheBeginningTheUniverseWas

You have a talent for teaching. Keep up the good job.

peterjohnson

He answered every question I had in mind except how he drew such a perfect circle

nicholasc

I had a friend who was very interested in art, and one of the things he did almost every day was practice drawing circles, straight lines, squares etc. Not for hours, mind you, but just 5-10 minutes each day. He obviously got very good at drawing these basic shapes without a straight edge, ruler, or compass.

Point is, if you want to have a skill, you have to practice it.

Name-psfx

I wish I had this guy teaching me maths in school I swear to god!

smithmeister

Kid coughs in 2015: carries on*

Kid coughs in 2020: everyone, get out get out!

khotsok

omg, he can make everything simple and easy, that's incredible!!!! congrats

mariazuza

I wish I had this teacher so captivating and willing to explain.

andrewfarquhar

This guy will get an OAM at some point in the future, I'm calling it now....

clintjoseph

First time, I am interested in Mathematics .
Super class

santhoshbejugama

Great video. Thought he was going to use Pythagoras Theorem after labelling points X and B.

OA^2 = OX^2 + AX^2
OA^2 = (OB + BX)^2 + AX^2, but OB = OA therefore
OA^2 = (OA + BX)^2 + AX^2
OA^2 = OA^2 + 2(OA)(OB) + OB^2 + AX^2
0= OA^2 + 2(OA)(OB) + OB^2 + AX^2
-2(OA)(OB) = OB^2 + AX^2
This is impossible because the sum of two squared number cannot be negative hence initial assumption must be wrong. Therefore tangent is always perpendicular to the radius of a circle it subtends.

Question: If I started out by saying, "By Pythagoras Theorem, OA^2 is IDENTICAL to OX^2 + AX^2 (sorry, I can't use the three line equal sign) would line 3 be sufficient to support the contradiction ?

petebola

I don't know if you're Australian but your accent, sir, is impeccable. As a British I am intrigued :D Sounds much better than the American accent.

cerenkoc.c

Correction: In proof by contradiction, you don't start with a false premise. You start with a premise you are testing.

murattanyel

I gotta subscribe. I love your accent. You sound so fancy.

ericBorja

lovely explanation this man is a maestro

bruce

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