pascals-triangle: split into instructions and introduction

[ErikSchierboom]

No description provided.

[ErikSchierboom]

Do we need more here? Some examples?

[BNAndras]

An example explicitly showing the addition process like in https://en.wikipedia.org/wiki/Pascal%27s_triangle#/media/File:PascalTriangleAnimated2.gif might be handy. I think that's where students might get stuck. Once you've got over that, I don't think additional examples provide a lot of extra insight. The modeled triangle doesn't change, just the number of rows exported.

[ErikSchierboom]

I couldn't come up with a story here. I'm open to suggestions :)

[jiegillet]

uh, I didn't even know you could comment on files, TIL.

Pascal's Triangle is a classic: here are some stuff you can do with it, maybe inspiration will strike:

• You can draw a Sierpinski triangle by coloring the even/odd numbers
• the sum of each row is a power of 2
• each element is a combination, entry k in row n tells you how many ways you can pick k elements from n
• squishing all the numbers in a row gives you a power of 11 (1331 = 11^3, 14641 = 11^4)

It's all a bit nerdy, but that can be a good thing :)

[ErikSchierboom]

I think the third one is most suitable for a story. Thanks

[IsaacG]

I had no idea there were so many things you could do with it!

[jiegillet]

Oh, there's more, there are so many patterns in these numbers. Fibonacci numbers are also hiding in there.

[MatthijsBlom]

Much more!

• An especially accessible list of patterns: Pascal's Triangle @ MathIsFun. Possibly interesting exercise: spot the duplicates. Most of the patterns listed here are really the very same pattern, just phrased in different ways.

• Skim the images in the Wikipedia article for hints at more patterns, elaborated on in the text.

[BNAndras]

An example explicitly showing the addition process like in https://en.wikipedia.org/wiki/Pascal%27s_triangle#/media/File:PascalTriangleAnimated2.gif might be handy. I think that's where students might get stuck. Once you've got over that, I don't think additional examples provide a lot of extra insight. The modeled triangle doesn't change, just the number of rows exported.

[ErikSchierboom]

@BNAndras I've added a bit more text, but so far struggled to visually and textually explain the logic. I'm open to suggestions.

[ErikSchierboom]

I've added a story and updated the instructions.

[ConeDragon]

After discussing about the "math is boring" part, I found this on line 3:
With the weather being great, you're not looking forward to spending an hour in a classroom doing math.

[kotp]

Style consistency for "single sentence per line" regarding a link given, the change will match the link on line 15 (prior to change being made).

Broke up the long line with the colon being a separator. While a single sentence, this is a reasonable exception to the strict "one sentence per line" and still supports the reason why we have that style adopted, I think.

[kotp]

Suggested change

	Whilst waiting for your math teacher to arrive, you can't help but notice some patterns in the triangle: the outer values are all ones, each subsequent row has one more value than its previous row and the triangle is symmetrical.
	Whilst waiting for your math teacher to arrive, you can't help but notice some patterns in the triangle:
	the outer values are all ones, each subsequent row has one more value than its previous row and the triangle is symmetrical.

[jiegillet]

After discussing about the "math is boring" part, I found this on line 3: With the weather being great, you're not looking forward to spending an hour in a classroom doing math.

I personally thought that this was fine, because one can enjoy math but still enjoy great weather more.
Maybe removing "doing math" could emphasize that this is really about the weather.

[ErikSchierboom]

I've updated!