Pascal’s Triangle, an interesting number patterns in mathematics.

ProtonsTalk ^ | Pravallika

[shobk]

Pascal’s Triangle has many applications in mathematics and statistics, including its ability to help you calculate combinations.

[shobk]

Hey, I read a very interesting article on Pascal's Triangle from a website named ProtonsTalk. Can someone explain any real-world application of this interesting topic?

[whitney69]

Wait for the comic book to come out. There is so little this is good for, I hope he spent all the grant.

One real life situation that Pascal’s Triangle is used for is Probability, and combinations. We have situations like this all of the time. For example, say you are at an ice cream shop and they have 5 different ice creams. You want to know how many different ways you can pick two of the ice creams and eat them. Both are fattening and will harden your arteries.

In mathematics, probability is defined as the extent to which an event is likely to occur, measured by the ratio of the favorable cases to the whole number of cases possible. Might be profitable if it is used at the race track if you bet a trifecta. Otherwise, eat what you have a taste for. By the time you figure out the formula, you’ll die of starvation.

wy69

[DoodleBob]

I read a few articles, and while it is interesting and has lots of cool properties, I don’t see it serving any material empirical/computational function. I think it is chiefly a beautiful thing in mathematics and God’s creation, which alone is valuable.

[Larry Lucido]

Welcome to FR.

Don’t be a “1 of” poster.

[KarlInOhio]

Once upon a time when the country was sane, you could use it to determine the odds of a specific grouping of sexes in children. For example if you had 4 kids the odds were:

4F 1/16
3F 1M 4/16
2F 2M 6/16
1F 3M 4/16
4M 1/16

But it doesn't work well with 53 genders.

[cicero2k]

A simple pattern that generates the irrational numbers such as the golden ratio along with prime numbers. Sort of an image of truth since math is irrefutable and the same all over the universe.

[ProtectOurFreedom]

“…math is irrefutable and the same all over the universe.”

Aren’t you the racist? I’ll bet you even expect students to get the right answer, too. Off to the CRT seminar with you to get your head straight!

[dayglored]

Welcome to FreeRepublic, and thank you for posting this thread. Although I knew of Pascal's Triangle, I learned a few new things about it reading the article.

Some hints, since you're a n00b:

• To avoid strange characters appearing in titles and comments, use plain ASCII characters for apostrophe and quotes, NOT the so-called "Smart Quotes" that look like 6's and 9's. They don't work well on FR.
• Don't just post the thread and run, or hide. We like to discuss! Take Larry Lucido's advice, and take part in the thread discussion.
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FRegards, Dayglored

[dayglored]

> ...math is irrefutable and the same all over the universe...

I believe those characteristics are true because Math is a description of the nature of Being. If it exists, then Math describes it.

I'm not a mathematician, but was trained in Physics, which is Math applied to the physical universe that comprises Objective Reality. Or as some have said, Math is the language in which Physics is written.

The fundamental inarguability of Math (and of Physics) is the basis for all else that we do and experience, whether we know and acknowledge it, or not. It is God's Gift to sentient beings.

There's an old (and vaguely profane) joke about what God's occupation must be, based on various parts of the human body. It misses the point. If indeed God has an occupation, then He is a Mathematician. All else follows from that.

[grey_whiskers]

+1

[dayglored]

> I’ll bet you even expect students to get the right answer, too.

There's a basic misunderstanding about "answers" when it comes to Math. [Caution, the following sounds pedantic but it's really meant semi-seriously.]

There is only one "answer" to a Math problem, and it's the one that is correct mathematically. Mathematically incorrect responses are responses, but they do not answer the problem.

The modern groovy, PC motto: "There are no wrong answers" is actually not far off. Because a wrong answer is not an "answer" at all, it's just a mistaken response. "Answering" something with hogwash might work in politics or psychotherapy, but in Math it's just wrong.

There are no "opinions" about a Math problem. There is an answer, and there is everything else which is not an answer.

So to address your comment, No I don't expect students to get the right answer, I mostly expect them to come up with incorrect responses. Teachers are supposed to correct that. I am pleased and delighted when they do get the right answer. :-)

[Savage Beast]

.

[algore]

I used to think that, but answer me this

8 / 2(2+2) =

I say it = 1 but consensus says I am wrong

https://www.popularmechanics.com/science/math/a28569610/viral-math-problem-2019-solved/

[alexander_busek]

Don’t be a “1 of” poster.

I suspect you mean "Don't be a '1-off' poster."

I.e., a "hit-and-run" poster.

Regards,

[dayglored]

It's a classic "order of operations" problem. The order that I learned is:

1. Operations inside parentheses (fractional numerator and denominator are considered independently parenthesized)
2. Powers, exponentials, logarithms
3. Multiplication and division, proceeding left-to-right
4. Addition and subtraction, proceeding left-to-right

So to solve 8/2*(2+2) (I added the * to clarify the implied multiply)

1. Add 2+2, so the parenthesized value is 4
2. All remaining operations are multiplication and division, so proceed left to right. 8 divided by 2 is 4, times 4 is 16.

To get your answer of 1, we have to make an assumption: that everything to the right of the division is the denominator of a fraction in which 8 is the numerator, i.e.:

8 / ( 2 * (2 + 2) ) = 1

In this case the "consensus" is about the rules of order of operations. Under the set of rules I learned, the correct answer is 16.

Note that if the problem had been written using fractional notation it would have been obvious immediately which interpretation was intended.

And FWIW, the above is a good example of why I prefer calculators that use RPN (Reverse Polish Notation, XY+) to AN (Algebraic Notation, X+Y). RPN is unambiguous and does not require parentheses; it's also the way computers actually do arithmetic operations (get X, get Y, add them).

[dayglored]

I answered your question above BEFORE reading the PopMech link you sent, so I see now that I duplicated some of the information in that article. Sorry for being long-winded. :-)

[Enterprise]

You are right. The answer is one. The way we were taught is that 8 is divided by a number. But what is that number? It is 2(2+2). Before you can divide 8 by the second number you have to determine its value, which is 8. If you separate the first 2 from the equation, it becomes a different equation with a different answer. For them to come up with 16 the question would have to read what is 8/2 X (2+2).

[dayglored]

And for the sake of completion, in my order-of-ops list I neglected one other thing, which is that along with fraction numerator and denominator being considered implicitly parenthesized, so are the things superscripted in an exponent. So for example:
  e^2x
The '2' and the 'x' get multiplied together before 'e' is raised to that power.

To make that clear in a single-line expression without superscripts, one would have to write:
  e^(2x)

[Still Thinking]

Agreed. That’s it’s even in question is an artifact of imprecise PC-era typesetting of expressions. If I saw that, I think I’d assume the (2*2) was intended to be a factor in the denominator, but strict PEMDAS says you’re right.

[Still Thinking]

Although, on further reflection, I have sometimes seen PEMDAS interpreted as P-E-M-D-A-S, as opposed to P-E-[MD]-[AS], which would give a result of 1.