triangle inequality question.. (1 Viewer)

[govich]

just a quick question guys

why is the triangle inequality a + b >= c?
why equal to?

i was doing the 2001 hsc paper again this morning and Q8a part ii says a,b and c are three sides of a triangle. surely if equality holds then they are three sides (?) of a straight line? and you no longer have a triangle (you no longer have 3 angles)? reason i ask is i was going through checking and i noticed that my solutions kinda fudged the working...

"If (b-c)^2 < a^2, then (b-c)^2 =< a^2."

i tried asking a few people today.. doesn't seem to make much sense.

oh and everyone doin the hsc tomorrow good luck

 

[Shuter]

Technically a strait line is a triangle or any polygon.

 

[govich]

Technically a strait line is a triangle or any polygon.

i would have thought a straight line is the one thing a triangle wouldn't be?

a straight line is the shortest distance between two points right. and a triangle is a three sided polygon with (funnily enough) three angles.

i'm about to ring up the advice line.

 

[govich]

OK i just called the advice line and worked through the question.

basically you end up with (b-c)^2 < a^2. the best explanation the man had was that you could then deduce that it's either less than or equal to simply because it's less than. but then if you have 3^2 > 2^2, could you just as easily change it to 3^2 >= 2^2? equality never holds? he agreed that it isn't really a satisfactory explanation and just told me to use greater than if it comes up again..

 

[Shuter]

i would have thought a straight line is the one thing a triangle wouldn't be?

a straight line is the shortest distance between two points right. and a triangle is a three sided polygon with (funnily enough) three angles.

i'm about to ring up the advice line.

I agree I would have just used greater than, but it's like 24^0 = 945^0 = 1. It can be both things, it's just a different form, it will still agree to all the rules of a triangle hence could be considered one, with two angles of 0 and one of 180.

 

[govich]

I agree I would have just used greater than, but it's like 24^0 = 945^0 = 1. It can be both things, it's just a different form, it will still agree to all the rules of a triangle hence could be considered one, with two angles of 0 and one of 180.

hehe fair enough. i suppose it depends on how you look at it. i don't consider 0 degrees to be an angle. oh well, i can't be convinced at the moment, and i'm not gonna try to argue any more..i've tried ringing teachers classmates advice line etc. everyone agrees. general consensus is to fudge

 

[Jase]

So Gov, you're asking why the equality holds? Well.. why can't it?

sum of two sides can equal the third. e.g. a triangle with side lengths 1, 2 and 3
1+2 = 3; 3+1 > 2

You should start off with the triangle ineqaulity with the equal sign already in, and keep working off that... but have you seen the book's solutions.. what's all that modding business?

and a straight line.. is NOT a triangle lol.

 

[govich]

rearranging the numbers doesn't count

draw me a triangle with sides 1,2,3 and i'll get a medal for ya in the morning.

maan i called mike and he agreed with me. you so can't win

 

[Shuter]

draw me a triangle with sides 1,2,3 and i'll get a medal for ya in the morning.

haha that's what I was about to say.

 

[mojako]

you cant just make a triangle with random sides

Well I think the third side is equal to the sum of the other two sides when the triangle approaches a straight line
we did this thing in complex number...

But, in the inequality
|a+b| <= |a| + |b| and |a-b| >= ||a|-|b|| , a and b real numbers
equality holds when ab>=0
theres a proof of this im cambridge, page 240

 

[Jase]

Sure you can, it might look slightly retarded. But it works. Gov I'll show ya my 1,2,3 triangle. in the morning.

|a+b| <= |a| + |b| is a triangle inequality? what does (a+b) mean? the opposite side of a and b or the sum of two sides a and b.

 

[mojako]

Sure you can, it might look slightly retarded. But it works. Gov I'll show ya my 1,2,3 triangle. in the morning.

|a+b| <= |a| + |b| is a triangle inequality? what does (a+b) mean? the opposite side of a and b or the sum of two sides a and b.

well then can u make a triangle with sides 1, 2, and 99999999999 ??
or 0.0001, 0.00000000000000001, 9999999999999999999

|a+b| <= |a| + |b| and |a-b| >= ||a|-|b||
is the complete version of triangle inequality, a and b can be complex

Cambridge proves that when a and b are real,
equality is reached when ab>=0

but when they're real they form a straight line
(remember vector addition...)

 

[govich]

Sure you can, it might look slightly retarded. But it works. Gov I'll show ya my 1,2,3 triangle. in the morning.

hehe if by slightly retarded you mean curved then ok

ps measuring while travelling at 0.9c doesn't count either

 

[Slidey]

All triangles are curved... geodesic.