Element of 10cm divided into 3 equal parts?

Hello

3.3333... is not an infinite number in mathematics. It cannot be expressed with a finite number of digits in base 10, but if we were to write it in base 3 for example, it would simply be 10.1 with a single digit after the decimal point.
On the other hand, 1/2, which is written as 0.5 in base ten, requires an infinite number of digits (0.1111111...) when written in base 3. And that doesn't mean that 1/2 is an infinite number. One must not confuse the (imperfect) representation of a number in a numeral system with the intrinsic value of the number.

As for cutting a real object into three equal parts, it is neither more nor less difficult than cutting it into two! Mathematical equality only belongs to mathematicians, while the equality of real objects is always approximate.

It is very simple with a ruler and compass to divide a given length into three without worrying about irrational numbers since we do not do any calculations.
The diseases of numbers are not transmissible to instruments (thankfully).
So, if you do not know the method of Thales usually used, here is another one that is more related to Pythagoras.
Draw the given segment (e.g., 10cm) and extend it by half (5cm).
At the beginning of this segment (point a), draw a perpendicular line and mark your compass opening on it (5cm). Close it all to obtain a triangle abc, right-angled at (a). On the base of this triangle, which measures 15 cm, draw two perpendiculars (at 5cm intervals) that divide this base into three and connect to the hypotenuse.
The largest of these two segments measures one third of 10 cm. (see the properties of isosceles triangles.)

First, you need to draw a perpendicular line to the segment
then place the point on the side where you took the perpendicularity in the middle of a segment formed by the perpendicular line, thus forming an isosceles triangle. Then, you need to apply the property of medians to find the center of gravity, which is equal to two-thirds of the segment, allowing you to divide it accordingly.

tends towards infinity Ok but an object is finite, so with a tolerance (rounding)
So if the same tolerance is applied to the 3 parts no problem they will be equal, same if you fold in 3

Thank you for this information!!!

So concretely, we could conclude that it is possible to divide an object of 10cm into 3 equal parts that would have a length of 10.1 in base 3 if I understand correctly?

Thanks anyway.

Bye.

Re,

There lies the entire problem we are facing. How can we obtain "finished" parts with mathematically infinite values?

Thank you.

Pierrick.

the universe is infinite but I have finished thinking (it tires me)

Hi,

Very well, hoping that others can provide me with more answers.

Bye.

In theory, it would be possible because it's a third of a value; if each share is 1/3, each part is equal!
In practice, it's not possible because our tools do not allow us to do so. Moreover, it has no interest!

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#define ZESTYR BOSS

Hello,
It is impossible to divide into 3 equal parts because that would mean assigning a finite decimal value to 4/3 since an object has finite dimensions.

10/3 does not approach infinity; it approaches 10/3, but 10/0+ approaches infinity.

a+

:S
I have another mind-boggling topic like this
If x created the universe and z created x who created z and so on ^^
Does the universe actually have boundaries?
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Best regards

If z created x, then z existed before x, so it is impossible for x to have created z!

Does the Earth have "borders"? As long as you don't fly over Afghanistan, you can keep going for a long time!
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#define ZESTYR BOSS