Course talk:MATH110/003/Groups/Group 05

Dear group 5,

The TA and I have reviewed your work. Here are our assessment of your work.

• Presentation: Good organization, readable.
• Mathematical content: The part about exponential functions and log functions are kind of inadequate. I think one could explore much more in the realm of exp(x), giving real life examples, interesting properties of the number e etc.
• Overall perceived effort: Put some effort in, could be better.

Hey everyone! After thinking about ideas about proofs, I really liked David's use of shapes to prove the Pythagorean Theorem.

My idea of an interesting proof would be:

How can the area of a Parallelogram be the same formula to find the area of a square or rectangle when a parallelogram does not contain 4 right angles within the shape?

I would like to take the concept of breaking down a parallelogram into shapes and angles and look at the properties all quadrilaterals share.

If we draw lines from one corner to it's opposing corner (creating a cross of the lines in the centre of each shape, we will find that we have 2 obtuse angles and 2 acute angles within the centre of the parallelogram, but we have four 90 degree angles within the square. We also have 4 triangles inside each quadrilateral. Note we also have 2 sets of parallel lines in each quadrilateral (top and bottom, sides). We can summarize all of this by saying we have 2 visually different shapes but how do be prove that Area=base*height for both the parallelogram and the square?

We can discuss the laws of opposing angles combined with the properties of a quadrilateral.

Any thoughts?

Hey Paige, sorry for the late reply, only saw this just then. I quite like this idea. Is there anything you would like me to do/add/research on? or mainly just your question of, "how do be prove that Area=base*height for both the parallelogram and the square?"

Hey, so yeah it needs to be on paper in some decent form of a project. not sure what you want to do with it? I only posted this like an hour ago or so, so no worries.

I will list properties of quadrilaterals and how 2 different shapes can become the same shape? if you want to write a list of maybe 4 or 5 questions we could 'ponder' about in this proof. and lets each come up with a proof so we have some material to compile in the morning and hand in. you can text me at 604.202.7843 if you want to discuss it that way.

Hey guys, just wanted to know how we wanted to approach the third part of our homework due tomorrow? Should we post our personal ability for the basic skills criteria and then from there, group them accordingly?

Hey Angus,

I made a subpage for our basic skills homework. I think we should just add our abilities and then organize them accordingly.

Your homework is written in a organized way and had consistent format throughout, that's great! However, what happened to question 17-25? Questions were listed for 17-20, but not answered. Questions 20-25 are missing. That's highly detrimental to your marks!

A few other pointers:

• Please write down more of your thought process/procedure of problem solving. After all, that's the most important aspect of this exercise.

• Please read the questions more carefully, try not to make any assumptions or jumping to conclusions. Give your answers a little more thought, check them first!