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|dw:1346864028370:dw|try drawing as many different tangents on this figure as you can

is it 3 ?

What point could you draw to satisfy that?

|dw:1346864106521:dw|

I count a whole bunch!

@UnkleRhaukus isnt it 3?

Can't you draw an infinite number through each vertex?

i count three infinite lines

ya different tangents

you could draw infinite tangents on any line segment technically, but that seems arbitrary

my doubt is why dont we count the tangent at the 3 vertices?

|dw:1346864223266:dw|

which way would the tangents at the vertices point?

Do we have to consider that the slope of a tangent at a sharp point is undefined?

i am not sure

a triangle is made with three tangents

so the answer is 3?

@CliffSedge that is basically how I figured it

If it's tangent to the triangle, then they cannot coincide with the sides of the triangle.

@CliffSedge y so?

Doesn't 'tangent' mean touch at only a single point?

@CliffSedge yes , but the tangent to a straight line is the straight line itself!!!

tangent is nothing but a flat approximation of curve!!

i see what i need to knw is this :|dw:1346864494173:dw|
can we draw tangent at point A?

i told the student i will answer it tmrw dats y i asked

agree @TuringTest can u answer my query above?

Is the slope of the tangent the always the same thing as the derivative?

The person who gave me this qn for presenting in lecture was @UnkleRhaukus and he has vanished :O

thats a nic reasoning @TuringTest

so can i tell the student that slope is not defined at sharp points ?

as a reason for no:of tangent=3 and not 6?

@TuringTest answer me pls

I say "yes" there are 3, but there is some debate, and I'm not perfect...

http://mathdl.maa.org/images/upload_library/22/Polya/07468342.di020721.02p01112.pdf

is see but i kthink u r right at this ,the calculus approach is best at this qn

A really good reference I would say that clarifies that tangents are not defined at edges.

thanks a lot evryone for sharing their ideas :")

nice link @siddhantsharan :)

Thank Google :D

Although they have not defined it precisely there. The precise definition is the calculus one.

@siddhantsharan that was really useful thx

the idea is derivative does not exist at sharp points

The slopes of the tangents need to be defined because the tangent
Is the slope at that Point

@CliffSedge The definition you are using is not the mathematical one.

Geometry is not mathematics?

Triangles are geometrical, lines are geometrical; how many hairs are we going to split here?

that definition makes no statement about sharp points, so it doesn't seem to help us here

False. It touches at P, but does not cross at P.

the vertex is only a single point it can only have one tangent

hmm now im not sure if it is one or zero

my point was that they intersect \(on\) the graph, at (0,0)

indeed, let me know if you find out something :)

its a good question