# Observable mathematical phenomena

• Mathematica
• pakmingki
In summary: Can someone please give and example of what this one is supposed to do. I'm not seeing anything particularly interesting going on here.

#### pakmingki

Lets share some mathematical phenomena that are just cool (for math people)

if you multiply any number of integers whose digits are only 1, the product will always be palandromic. Grab a calculator and see for your self. I would be really interested to see a proof for this phenomena.

heres another one, you;ve probably heard of it before.
take a 4 digit integer. All are > 0, and a maximum of 3 of the digits can be equal.

rearrange the digits in such a fashion where the integer abcd has the property a>b>c>d.

abcd - dcba = a 4 digit integer

Repeat over and over and see what happens.

I would also very much like to see a proof for that.

pakmingki said:
if you multiply any number of integers whose digits are only 1, the product will always be palandromic.
That's only true if the numbers are sufficiently small. The proof of when it works is "obvious" from the multiplication algorithm:

Code:
  1111
x  111
------
1111
1111
1111
------
123321

but when the numbers are large enough, you will overflow a digit and will no longer be palindromic. For example, open window's calculator, enter in a number with eleven 1's, and square it.

Hurkyl said:
That's only true if the numbers are sufficiently small. The proof of when it works is "obvious" from the multiplication algorithm:

Code:
  1111
x  111
------
1111
1111
1111
------
123321

but when the numbers are large enough, you will overflow a digit and will no longer be palindromic. For example, open window's calculator, enter in a number with eleven 1's, and square it.

Indeed, it is only palindromic with operations within 9 digits.

pakmingki said:
if you multiply any number of integers whose digits are only 1, the product will always be palandromic. Grab a calculator and see for your self.

I don't get it. I grabbed a calculator and entered in a number of integers whose digits are only 1.

9*8*7*6*5 = 15120. Thats not palindromic... What am I doing wrong?

DieCommie said:
I don't get it. I grabbed a calculator and entered in a number of integers whose digits are only 1.

9*8*7*6*5 = 15120. Thats not palindromic... What am I doing wrong?

9,8,7,6,5, are integers with only one digit, not numbers whose digits are only 1: i.e. 111 is a number which satisfies the criterion.

ahh, I knew I wasnt comprehending it right. Thank you.

pakmingki said:
heres another one, you;ve probably heard of it before.
take a 4 digit integer. All are > 0, and a maximum of 3 of the digits can be equal.

rearrange the digits in such a fashion where the integer abcd has the property a>b>c>d.

abcd - dcba = a 4 digit integer

Repeat over and over and see what happens.

Can someone please give and example of what this one is supposed to do. I'm not seeing anything particularly interesting going on here.Edit: Ok the digit sum of the result is always 18, is that it?

Last edited:
If we take a number like: 1244 = 1000 +2*100+4*10+4. Then if we take this Modulo 9, we get 1244 ==1+2+4+4 Mod 9.

So that rearranging these digits doesn't change the value Modluo 9, so that the difference between this number above, and one with the same, but rearranged digits is always divisible by 9.

I don't know if this is what parkmingki had in mind.

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## 1. What are observable mathematical phenomena?

Observable mathematical phenomena are patterns, relationships, and structures that can be observed and studied through mathematical methods and techniques. These phenomena can be found in various fields such as science, finance, and engineering.

## 2. How are observable mathematical phenomena different from abstract concepts in math?

Observable mathematical phenomena are different from abstract concepts in that they can be observed and measured in the physical world. Abstract concepts, on the other hand, are purely theoretical and do not have a tangible representation in the real world.

## 3. Can observable mathematical phenomena help us understand the natural world?

Yes, observable mathematical phenomena can help us understand the natural world by providing us with quantitative data and models to describe and predict natural phenomena. For example, mathematical equations and formulas are used to understand the motion of objects in physics.

## 4. What are some examples of observable mathematical phenomena?

Some examples of observable mathematical phenomena include the Fibonacci sequence, fractals, the golden ratio, and the Pythagorean theorem. These phenomena can be observed and studied in nature, art, and architecture.

## 5. How do scientists use observable mathematical phenomena in their research?

Scientists use observable mathematical phenomena in their research by analyzing data and creating mathematical models to explain and predict natural phenomena. They also use mathematical principles and theories to design experiments and test hypotheses in various fields of study.