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By Jove! I just dropped my seventh calculator, and now it's telling me that a circle with an area of nothing has radius 3. You know that:

  • The calculator calculates perfectly well
  • The calculator's display isn't broken
  • The calculator's buttons work properly
  • "Nothing" isn't , by Jove!
  • π is not 0
  • I am looking at the calculator display as I normally would (not rotated or reflected in any fashion)
  • The calculator is not in an error state (e.g. caused by division by zero, syntax errors)

How could this happen?

Hint:

What you're looking for means "nothing"

Hint #2:

What you're looking for is less than 5 letters long

Hint #3:

Commutative property of multiplication

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  • $\begingroup$ When you dropped your calculator the 'wiring' got crossed, now π inputs 0, so πr^2 always equals nothing $\endgroup$
    – TCooper
    Mar 5 '20 at 23:23
  • $\begingroup$ This seems way too broad. There appear to be many possible answers, and no real way of knowing which one is the intended one. $\endgroup$
    – Deusovi
    Mar 6 '20 at 5:13
  • $\begingroup$ @Deusovi I've edited the question to resolve some of those ambiguities. $\endgroup$
    – Avi
    Mar 6 '20 at 14:35
  • $\begingroup$ Are you by any chance rot13(Ebzna)? $\endgroup$
    – Mohirl
    Mar 6 '20 at 17:28
  • $\begingroup$ @Mohirl rot13(Gung vf irel yvxryl, ol Wbir!) $\endgroup$
    – Avi
    Mar 6 '20 at 17:29
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The answer is that nothing is:

nIX (synonym for nothing)

Explanation: You are from

Rome

as you use expressions like 'by Jove',

which reminds us of Jupiter/Jove, the Roman god.

As such, your calculator is a bit unorthodox.

It allows entry of pi (because you are a smart Roman who knows about such things, unlike most around you), as well as Roman numerals.

So on to your conundrum...

You know that pi r squared can be used to calculate the area of a circle. Again, you are quite smart. Now, you have a circular swimming pool of radius 3, and would like to know the area of said pool, to determine how many fish it will hold (your guests like to eat grapes and swim with fish). You pull out your Roman Calculator and happily punch in pi (which appears like a lowercase 'n' on the digital display) and multiply it by 3 squared.

Now Roman numerals do not have digits, so the calculator does the best it can; it returns the result as pi * 9, which of course renders again as that "n" followed by "IX". This is similar to an algebraic number like 9x, except it is 9pi, and the pi is in front. Putting pi in front is an anomaly of the Roman calculator, but perfectly legitimate given the commutative property of multiplication.
You study the output, eager to head to the fish store. Wait?! "nIX"? Nothing??? How can the area of the pool be nothing? The calculator seems to work fine. III times III is still IX. The wires are still connected. What could be wrong???

Baffled, you turn on your Roman computer and head to stackexchange to find out.

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  • $\begingroup$ I love this edit! It makes it 100% clearer as to what your answer is! +1 $\endgroup$ Sep 29 at 14:23
  • $\begingroup$ Precisely what I was going for :) $\endgroup$
    – Avi
    Sep 29 at 17:36
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PRE-EDIT - It could be because

It says E for error and you're looking at it upside down.

Because

Depending on the type of calculation, dividing anything by zero gives an error.

Thoughts

Wasn't sure if you were looking at the answer on the floor. :)

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The answer depends on

  1. The part of the calculator that is defected

    • The circuitry (unlikely as it can be turned on)
    • The buttons (some of them)
    • The display (assuming 7-segment LCD)
  2. How you tried to find the area and radius of a circle

    • Starting with the radius, $\pi r^2 = A$
    • Starting with the area, $\sqrt{A/\pi}=r$

As none of this specified in the question, the following will only consider the display being defected and try to address both cases of the calculation.

Case 1: $\pi r^2 = A$

It could be that only the last digit (units location) of the seven segment display is working. So, assuming you enter $r=20153$ as the radius, you could only see the last number, $3$. Typing the rest of the formula should yield $1275937150.0183146$, i.e., $1275937150$ on a 10-digit seven segment display from which you could only see the last digit, $0$.

Case 2: $\sqrt{A/\pi}=r$

It could be that only the first digit of the seven segment display is working and the rest just shows nothing (as opposed to a zero). So, assuming $A=31.4$, you could have tried to type the number and ended up seeing nothing then the rest of the calculation is supposed to give you $3.161475988...$ and since only the first digit is working, you get to only see 3; the rest of the decimal digits of the calculator shows nothing.

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From the references to

Jove

I suspect you might be

A Roman

Although I'm not 100% sure what to do with that.

Perhaps you've dropped

One of the beads from your abacus (maybe the 7th column?), and the abacus now reads nothing instead of the 30 it originally showed as the area.

This seems a bit weak though, I suspect there's more to it

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  • $\begingroup$ This isn't it. There is a logical progression between A = nothing and a radius of 3 that my calculator computed. The feature you've identified is a necessary calculation. $\endgroup$
    – Avi
    Mar 6 '20 at 17:42
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I propose that the answer is:

$o$ or simply zero.


In the Greek numeral system:

$o$ was used to denote zero:

Hellenistic astronomers extended alphabetic Greek numerals into a sexagesimal positional numbering system by limiting each position to a maximum value of 50 + 9 and including a special symbol for zero, which was only used alone for a whole table cell, rather than combined with other digits, like today's modern zero, which is a placeholder in positional numeric notation. This system was probably adapted from Babylonian numerals by Hipparchus c. 140 BC. It was then used by Ptolemy (c. 140), Theon (c. 380) and Theon's daughter Hypatia (died 415). Coincidentally, the zero value cell marker was the letter "ο" (omicron).

Emphasis mine.

I originally wanted to say:

$λ$ or lambda, since the area of a circle with a radius of $3$ is $28.27$. The value of the Greek numeral $λ$ is $30$, so rounding up would make it work. Additionally, in language theory and computer science, $λ$ is used to denote an empty string. However, this doesn't meet your requirement of "less than 5 letters".

Also, did you know that:

$2827$ appears in the first one million digits of $π$, 6 times? Almost meets the title of the puzzle well, no?

Additionally, in mathematics:

The following values can be used to represent nothing: $null$, $nil$, $NaN$, $⊥$, $↑$.

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