Higher Math Thread - Pascal's Triangle

Exercism
1

The linked instructions do not use this word.

If there is any ‘mathematically conventional diagram’, then I expect it to be the second one.

As far as I know there is no actual convention here. At best there is a way the triangle is usually drawn, i.e. most frequently – for whatever reason.

See also: the wikipedia article.

Unsure what this should mean exactly, but almost certainly: no, there is no such lingo.

I, of mathematical background, am continuously confused about what laypeople mean by ‘higher math’. Maybe it’s like with tall people: there is no qualitative difference between ‘tall’ people and non-‘tall’ people, and moreover there are ‘tall’ toddlers.

Something like this, by the way, is one of mathematic’s core purposes. If it is not understandable then it isn’t proper math.

This link bothered me as well. The most useful insight is obscured:

Pascal’s formula shows that each subsequent row is obtained by adding the two entries diagonally above,

(n; r)=(n!)/((n-r)!r!)=(n-1; r)+(n-1; r-1). 265x41

2

Maths especially used at higher altitudes. Or those typically taught are higher levels of education. Merriam Webster defines it as,

mathematics of more advanced content than ordinary arithmetic and algebra, geometry, trigonometry, and beginning calculus

While this may not be a rigorous or well defined term, nor a term used by mathematicians, I do believe this is a pretty well understood term in common parlance.

3

With ‘higher math’ thusly strongly culturally defined,

becomes almost tautological. After all, if a specific mathematical subject were commonly studied then it wouldn’t be considered ‘higher’ math.

(Not that I object to what you are saying, @IsaacG. At worst I lament the common usage of the term, or perhaps even that it exists.)

4

I think that’s exactly what it’s supposed to mean :smile: Higher math is math which is higher than what the average person knows. That may be less a tautology and more … by definition. (I think definitions and tautologies are different, at least!)

5

To me, ‘higher’ suggests either or both of

  • greater prestige
  • less foundational / less basic / less simple

I object to ‘higher’ because

  • while ‘higher math’ does enjoy greater prestige, some parts of it do so only through association with ‘higher education’ and not through merit. Lots of subjects could (or even should) be taught to primary school and high school students, but somewhat arbitrarily just aren’t. Not all of ‘higher’ math’s prestige is deserved.
  • ‘higher math’ does not, generally, build upon, eh, ‘lower math’. Moreover, there are ‘higher math’ subjects that are entirely unrelated to everything commonly taught. Some ‘higher’ math might actually be ‘lower’ than some commonly taught math.

Which is to say: I feel the adjective ‘higher’ is inapplicable to what ‘higher math’ is commonly understood to refer to. (A term with a similar problem: red herrings are neither red nor herrings.)

1 Like
6

5 posts were merged into an existing topic: Error in Pascal’s Triangle

10

This is the change we’re proposing: replace “by adding the numbers to the right and left of the current position in the previous row.” with “by adding the two numbers diagonally above”.

I and tasx agree with this, what about @MatthijsBlom?

12

Nope, we’re not. What does @ErikSchierboom think?

13

Based on what MatthijsBlom did and didn’t say, I think we two are in agreement that the instructions are quite clear as is. However, there’s something like 125 Exercism team members and maintainers who may be present on this forum and reading the thread, who may yet chime in. There’s also hundreds if not thousands of other Exercism members who may want to chime in, as well. While they may not be a decider on the PR, we’re definitely interested in their opinions and discussions.

1 Like