how many trianles can be formed by conceting the dots in the diagram?

[echo elbow]

justfy with words and calculations

[warm iron]

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[echo elbow]

<@&1309522179368419349>

[still valve]

What is required to make a triangle?

[echo elbow]

You need to convey the dots but I’m not 100%sure

[still valve]

Which dots?

[echo elbow]

^

am i wrong to asume that it is 12

@still valve

[still valve]

You're always wrong to assume.

[echo elbow]

why

cuz is it not 3x12

[still valve]

Because we do not assume in math, we prove.

[echo elbow]

ohhh i like that

but do youi understnad the question cuz its owrded alittle poorly

[still valve]

,rotate

[still valve]

I believe so. It's asking how many unique triangles exist that have the given points as vertices.

So then the question is, what are the necessary and sufficient conditions for a set of vertices to form a triangle?

[echo elbow]

no clue

[still valve]

Do you know what a vertex is?

[echo elbow]

yeah

[still valve]

What is a vertex?

[echo elbow]

the point where they conect?

[low shoal]

Yes or the corners

[low shoal]

Try looking at the diagram. How many vertices should there be such that a triangle can form? Think about how one vertex can account for more than one triangle

[echo elbow]

yes

[still valve]

So then what is the requirement for a group of vertices to form a triangle?

[glad matrix]

Lets classify the dots as
1 Junction dot
4 Horizontal dots (H)
3 vertical dots (V)

Ypu need to pick 3 vertices for the triangle

Case 1: If you dont use junction dot, you need to pick 2 H dots and 1 V dot or 2V dots and 1 H dot.

Case 2: If you use Junction dot, you need to pick 1 H dot and 1 V dot.

[echo elbow]

But there is no way to make it with 2h and the junction dot right

[echo elbow]

But how would I calculate this

[livid vapor]

yea which is why you need to pick one H and one V

[livid vapor]

do you know combinatorics?

stop trying to manually count and just use that

[livid vapor]

this is already a huge hint here

[still valve]

Why not?

[echo elbow]

Because it is now a straight line

[echo elbow]

Yeah I do

[livid vapor]

just use combi

[echo elbow]

I don’t know how to

[still valve]

Right, and that's exactly the condition on the vertices of a triangle I was trying to get you to realize; a set of three noncolinear points.

[livid vapor]

actually better idea let techie cook

[echo elbow]

Like what formula would I use

[echo elbow]

I understand how to do the formula but I’m not sure on how to apply it to this shape

[echo elbow]

That’s if I want a diagonal

@still valve

[still valve]

... what?

[echo elbow]

So if I want so let’s say make a straight line from a octogong

I would use this method

I have the wander by counting but I need to figure out the method

It’s 24

[still valve]

It's not 24.

[still valve]

Why?

[echo elbow]

How because I can’t make another different triangle

[echo elbow]

That’s what my teacher is saying and I’m not sure why

[still valve]

Are you interested in learning why?

[echo elbow]

Yeah I am

[still valve]

Okay, so, how many vertices does an octogon have?

[echo elbow]

8

[still valve]

And how many vertices does a line segment have?

[echo elbow]

2

[still valve]

Get it?

[echo elbow]

Yeah but how would I use that with this question

[still valve]

(Of course, not all of those pairs of vertices are diagonals, some of them are sides.)

[echo elbow]

Yes

Yeah and we need to eliminate them

Or else we would have duplicates

[still valve]

What are the necessary conditions for a set of vertices to form a triangle?

[echo elbow]

3

[still valve]

...and?

[echo elbow]

But they can’t All be in the same line

[still valve]

Right, so how many lines do we have here, with how many points on them?

[echo elbow]

What do you mean

[still valve]

...I mean... the points... can't all... be in a line. So which points... are all in a line?

[echo elbow]

You have 1 junction point

3 vertical ones going down

And 4 horizontal going to the right

[still valve]

...can you... count?

[echo elbow]

Yeah we are excluding the junction point

[still valve]

Why? I didn't say to.

[echo elbow]

Ok then it’s a 5x4

[still valve]

And if we exclude the shared point from one of the lines, what do we get?

[echo elbow]

I’m not sure what you mean

[still valve]

We want. To count. Sets of three points. So we do not. Want to count. The same point twice.

[echo elbow]

Yes I got that

[still valve]

You are counting a point twice.

[echo elbow]

Am I counting the junction twice

[still valve]

What is "the junction"?

[echo elbow]

+close

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