Me and my three siblings

Question

First attempt at making a riddle, it should be easy for you guys.

One of my siblings idolizes me, constantly trying its best to look like me, which I gladly appreciate.
He even settles down the quarrels between me and the two others siblings, I'm sure they're just jealous of my current position.

Combining our efforts, my beloved sibling and I can easily draw a circle and a square. The two others can too, but in my opinion, our square looks better.

I absolutely need my partner for making the circle and the square, same thing for the two others, else it's not possible if we're alone while doing these.

Our full family is renown internationally, and we have many cousins.

Question : Can you identify me, my family, and the group of four siblings ?

Hint 1 :

When we make a circle, we effectively rotate around a base once.

Hint 2 :

When all 4 of us regroup for calling out someone, we find out that 1 called person out of 3 turns out to be one of our cousins.
Also, regrouped, we can't draw any circle nor any square.
...
It turns out that we can draw, with some twisting, 1 circle, 2 circles, or a square, when we are regrouped.

Hint 3 :

I'm on almost everyone's hands.

Hint 4 :

You can count on me at any time... Except for science, it bores me.

Hint 5 :

Here I am now.

Answer 1

I'd guess 2,3,5,7.

Clue 5 tells us that

the narrator is 5.

One of my siblings idolizes me, constantly trying its best to look like me, which I gladly appreciate.

This would be '2', which looks like an upside-down '5'.

He even settles down the quarrels between me and the two others siblings, I'm sure they're just jealous of my current position.

The 'differences' between 5 and either 3 or 7 'are' 2; the position of 5 is exactly between 3 and 7 (but I'm not sure why that would be something to be jealous of).

Combining our efforts, my beloved sibling and I can easily draw a circle and a square. The two others can too, but in my opinion, our square looks better.

$5^2=25$, which is a perfect square. The 'siblings' 2 and 5 even form the digits of the square. We have $7-3=4$, which is also a perfect square, but it doesn't contain the digit 7 or 3, which may cost points in a narcissistic accounting.
$5 \cdot 2 = 10$, which contains a circle. Also, $7 + 3 = 10$, which contains the same circle.

I absolutely need my partner for making the circle and the square, same thing for the two others, else it's not possible if we're alone while doing these.

None of 2,3,5,7 is a square, and none of them contains a circle.

Our full family is renown internationally, and we have many cousins.

The primes.

Question : Can you identify me, my family, and the group of four siblings ?

Narrator: 5; family: primes; siblings: 2, 3, 5, 7.

Hint 1 : When we make a circle, we effectively rotate around a base once.

Not sure about this. Base 10?

Hint 2 : When all 4 of us regroup for calling out someone, we find out that 1 called person out of 3 turns out to be one of our cousins. It turns out that we can draw, with some twisting, 1 circle, 2 circles, or a square, when we are regrouped.

Regrouping: adding up in various combinations of 0, 1, 2, 3 or 4 of these numbers to get the set of 12 numbers: {0,2,3,5,7,8,9,10,12,14,15,20}. There are 12 numbers, of which 4 are the siblings, so 4/12 or 1/3 of them are the siblings.
Geometric shapes: 0 has 1 circle, 8 has 2 circles; 0 is also a perfect square.

Hint 3 : I'm on almost everyone's hands.

Most people have 5 digits (cf the narrator) on each hand.

Hint 4 : You can count on me at any time... Except for science, it bores me.

'5' is a number, which one can count at any time. I'm not sure why science bores the number 5.

Hint 5 : Here I am now.

This points to the narrator: '5'.

Answer 2

My guess is

The family is:
Geometry box

The four are:
Compass
Divider
Protractor
Set Squares

Compass and Divider are looks like same
By using Compass, Protractor can draw Circle
By using Set squares can draw Square

---

My Other guess is:

The family is:
Trigonometric functions

You are
$\sin \theta$

Your siblings are
$\cos \theta$
$\tan \theta$
$\cot \theta$

Using the $\sin \theta$, $\cos \theta$ we can create circle and square.

Answer 3

Could it be you are:

The middle finger

Your siblings are

The index finger, ring finger, and pinky finger (thumb is technically not a finger?)

One of my siblings idolizes me, constantly trying its best to look like me, which I gladly appreciate.

The ring finger curls atomatically when the middle finger curls

He even settles down the quarrels between me and the two others siblings, I'm sure they're just jealous of my current position.

Not 100% sure on this one, maybe something to do with it being the ring finger

Combining our efforts, my beloved sibling and I can easily draw a circle and a square. The two others can too, but in my opinion, our square looks better.

The index finger and middle finger together could draw a circle and square and it would look a lot better than one drawn with the rind and pinky fingers

I absolutely need my partner for making the circle and the square, same thing for the two others, else it's not possible if we're alone while doing these.

A single finger cannot draw anything since it can't hold a pen/pencil

Our full family is renown internationally

Not sure about this one

and we have many cousins.

Toes and thumbs might be considered cousins of the finger

Hint 1:

When we make a circle, we effectively rotate around a base once.
-The base is the wrist, which rotates once effectively when drawing a circle

Hint 2:

When all 4 of us regroup for calling out someone, we find out that 1 called person out of 3 turns out to be one of our cousins.
-Not sure about this one, but calling out someone could be giving the middle finger
It turns out that we can draw, with some twisting, 1 circle, 2 circles, or a square, when we are regrouped.
-Again not too sure about this one

Hint 3:

I'm on almost everyone's hands.
-Fingers are on almost everyone's hands, except those who have lost their fingers in an accident or birth defect etc.

Answer 4

Partial answer, I can't figure out the whole thing, and I'm not convinced I'm on the right track:

The narrator is

Pi, $\pi$, $3.141592...$

The beloved sibling is

Square root of two, $\sqrt{2}$, $1.4142...$

The other siblings are

Tau, $\tau$, $6.2831...$, and Pi/2, $1.5708...$

Tries its best to look like me:

Both $\pi$ and $\sqrt{2}$ are irrational, but $\pi$ is transcendental as well, which $\sqrt{2}$ isn't, so it "tries its best" but doesn't succeed.

He settles down the quarrels between me and the other family members:

The other members are $\pi$ times, or divided by, $2$.

They're jealous of me and my position:

There is some movement to replace $\pi$ with $\tau$ in mathematics, but this is mostly ignored.

My sibling and i can draw a circle and a square:

$\sqrt{2}$ is the diameter of a square the sides of which have length 1, and the length of the upper/lower half of a circle around the center of a line of length 1 is $\pi$ each.

The others can too, but our square looks better:

Not sure. Probably it's easier/cleaner to draw a square using Pythagoras.

Our family is renown internationally, and we have many cousins

Everybody knows maths worldwide, and there are many more numbers.

Answer 5

Are you:

The list of (first four) prime numbers 2,3,5,7...

The narrator is

The number 2

The beloved sibling is:

The number 7 (Tries to look like 2)

You family is:

The list of prime numbers.

Our full family is renown internationally, and we have many cousins

The list of primes is well known subject

Hint 3:

I'm on almost everyone's hands: Numbers are digits.

You can count on me at any time... Except for science, it bores me.

You can list (count) the prime numbers, although it is not very exciting except in the sciences, of which it is rather important.

As for the shapes:

I was trying all sorts of different ways to visualise making the circles/squares using the appearance of the numbers, or their products, or something similar, but couldn't get there. Maybe this or another number sequence?

Answer 6

My guess (probably totally off-base): The family:

The integers mod 12.

The siblings:

The numbers 2, 3, 4, and 9

You are:

2

My reasoning is as follows (Using mathjax spoils the spoilers; sorry that it looks so nasty):

You used the word 'regroup' and 'group'; regroup seemed like it was hinting at something - a group! Rotating around a base reminded me of modular arithmetic, like a clock.

The squares and the circles:

The thing about 2 and 3 is that neither can generate the group Z12; neither can 4 or 9. However, they can together; my guess is that's what it means by making a circle. 3-2 = 1, which is a square; 49 is 1, which is also a square, albeit clunkier. I note that 4 and 9 form squares by itself, which is a problem.

The quarreling:

3 looks like 2, just an extra curve at the bottom, and it is between 2 and the other two numbers.

The cousins:

The numbers are mod 12, meaning that they have a lot of cousins, ex 0 has cousins 12, 24, etc. Mod 12 is the international standard for time as well.

Revolving around a base:

I mentioned that revolving around a base sounded like modular arithmetic.

The hand:

Like Steven Richard Oakes suggests, the numbers are all digits, which are on people's hands; 'you can count on me at any time' seems to refer to time, which is mod 12.

The regrouping

There are four numbers; if we choose an integer there is a one in three chance it's a cousin of one of the four. Not sure about the last hint.

Answer 7

I'm not sure what the sequence is, if this is a correct answer. I am thinking you are:

The numbers 2,4,5,6

The narrator is

The number 2

The beloved sibling is:

The number 5 (Looks like 2 upside down?)

He even settles down the quarrels between me and the two others siblings, I'm sure they're just jealous of my current position

I still have no idea what the 'quarrel' is.. :( I can only think the position refers to being first?

Combining our efforts, my beloved sibling and I can easily draw a circle and a square:

2 * 5 = 10 (The circle is 0, the numbers 'revolving' around base 10. 2,5 written together is 25, a square.

I absolutely need my partner for making the circle and the square, same thing for the two others, else it's not possible if we're alone while doing these.

Same thing goes for 4,6, which similarly makes 10 and 64 (8 squared, but backwards).

You family is:

I don't know what the 'family' refers to.. decimal numbers?

Hint 3:

I'm on almost everyone's hands: Numbers are digits.

Hint 4:

You can count on me at any time... Except for science, it bores me. A reference to counting with numbers?

Hint 5:

Perhaps you are suggesting the narrator is '5'. Hmm..

Answer 8

Now let's get the full explanation :

Narrator is

the figure 5

His loved sibling is

number 2, mirroring perfectly 5 on a 7-segments display, but not perfectly elsewhere.

The quarrels

5 is in the center of the numeric pad, 7 and 3 (and 9 and 1) are cornering 5. but 2 gets between 5, 7 and 3 to "protect" him.
$5 + 2 = 7$
$5 - 2 = 3$

Drawing

2 and 5 :
Square : $25 = 5^2$
Circle : $2*5 = 1$o

3 and 7 :
Square : $7-3 = 2^2$
Circle : $3+7 = 1$o

25 is greater ("better") than 4.
(I could have said that 2 can help anyone to make a square, and 3 help anyone to make a cube...)
Anyway, all alone, no one is able to make a square nor circle on its own.

The family & the group of 4 :

Prime numbers. "many" was an understatement, since there is an infinity of them.
The group of 4 are the only single-digit prime numbers.

Hint 1:

It could be interpreted in two ways : either it is the 0 found in 10, or it is one cycle around base 10 that makes 10.

Hint 2:

When regrouping 2, 3, 5 and 7, we can "call out" a 4-digit number.
out of the 24 combinations, 8 of them are prime (1/3 of them).

$2357, 2753, 3257, 3527, 5237, 5273, 7253, 7523$ --> prime

Square : $(3+7)*2 + 5 = 25$
One Circle : $(3+7)/2 + 5 = 1$o
Two Circles : $(3+7)*(2+5) = 1$oo (also a square)
or $2+3+5+7 = 2$o (2 cycles around the base 10)

Sorry, this wasn't a good hint, since you would need the solution beforehand...

Hint 3:

Everyone has 5 digits in their hands ...... almost...

Hint 4:

"count on me" refers to 5 being a number.
"Science Bores me" because on the periodic table, 5 is Boron.

Hint 5:

Until now, no "5" were found in the question, albeit 2 and 3 were already present.

Answer 9

I don't know enough about the subject to formulate a proper answer, but maybe this will provide a clue.

I think you are time, or the continuum spacetime. I think your family is the theory of general relativity and I think the group of siblings are the 4 dimensions.

Answer 10

Wild stab:

Integers (Decimals) 2,3,4,5 .....

Reason:

None. Just a shot in the dark.