Tarte--Math--Pascal's Triangle--challenge-prize

If you need help deciding if you want a prize: http://www.youtube.com/watch?v=F63DPiE5VCQ

Category:

Education

Tags:

• Edward Tarte
• math
• math puzzle
• math challenge
• math lesson
• Pascals Triangle
• square numbers perfect squares
• number patterns

[MaxReason]

It's implied but the constraint should be explicitly stated, that the paths to a given box may never be up; that you can only traverse down to the left or down to the right, never up-left nor up-right. Otherwise the number of paths is infinite.

Another way to express this is that given a row, the next step must be to a row below the current row.

[edwardtarte]

@MaxReason, I said it, explicitly, at 1:27: "following those paths, downward, from the top". So a person who listens to me carefully will probably not be inclined to make a comment such as yours.

[TheINTPMagician]

I see the pattern in the triangle... just not why... after a few days (so people have a chance to figure it out) can you explain it to us?

[edwardtarte]

@TheINTPMagician, go to my profile page and message me where you see the pattern. Then if you want a hint about why, I can probably give you one. For now, I don't want to explain it to all, because I want this puzzle to remain available.

[blackplatypus]

Recreational mathematics is awesome.

btw, has anyone ever noticed that if height = A and radius = Z

Then the mathematical volume of a Pizza is PiZZA?

[edwardtarte]

@blackplatypus, very clever. That reminds me: write 3.14 on a piece of paper so that when you perhaps hold it up to the light you can see it from the back. Write the 4 as it appears here in print, with the top closed instead of open. Then look at the 3.14 from the back. What do you see?

[green10goo]

@edwardtarte I don't understand, could you explain a little more? where do you write the second 4? and at then end, when you say "back" do you mean the same back where you wrote 4 again, or turn it around to the 3.14?

[skilespaul]

I will admit that I never did well in math, in school. At about the age of 10, I started needing glasses to see, but I never got glasses until I was about 13. By that time I was far behind the other kids in math, because I couldn't see what was written on the chalkboard well enough. Because I was so far behind, some math teachers treated me like I was stupid. therefore I developed a dislike for math, which lasted years. However, I found this video very interesting. Ed does a great job teaching.

[11889music]

Wait..... How do I pause?

[BIJMOZ]

I'm way past my math class days but this was really interesting :)

[Kargoneth]

Woah... I was looking up Pascal's triangle on Wikipedia and they mention Pascal's pyramid and Pascal's simplex. The latter two of which are much harder to draw on a two-dimensional surface but can still be visualized.

Darn it, Ed. You make me intrigued by such things!

Pascal's triangle even contains my favourite number sequence: (0), 1, 3, 6, 10, 15, ...

Sadly, as your video points out, it doesn't contain the sequence for my favourite curve, the parabola. I will *make* it contain it!

[Kargoneth]

@Kargoneth

*You're an audiophile

[Kargoneth]

An audiophile of my selection? Can you email yourself to me, Ed? You're and audiophile, aren't you? :)

(Oh ho ho! So punny!)