Strictly speaking, a name like "gobbledegook" is a symbol. That's a reasonable systematic, and important to note as a derived grapheme might strive for similarity with the name. Thus it becomes apparent that you are basically asking for how to name things, equivalent to the question of how does language work. In the same vein we see that maths does have aspects of language. That's true all the more if you are asking for a logical system of naming, if logic is a basic tenant of maths, though one might argue that it's foundational and maths is what's building on top. Naming, eh? The distinction is not very important, actually.
I will just focus on high-school maths for a quick answer.
The name Pi for the ratio of square area to area of a circle where the radius equals the square's side-length--to stay with your example--was an abbreviation of the Greek word perimeter. We see that the definition doesn't need to rely on the perimeter.
The choice of Greek letters might stem chiefly from the need to choose symbols that type foundries and print shops had already in stock, and it might have been traditional already prior to printing, but the decision for a name from natural language is well descriptive. All letters of the various common alphabets are already reserved for common constants and variables, not even uniquely, rather overloaded with meaning depending on subfield, or assigned arbitrarily by any individual author. On the other hand many function names have longer abrevs. That's the important point, in my humble opinion, as the trend in professional programming, probably the biggest field in applied maths, goes to speaking variable names. A multiletter grapheme like gobbledegook is still a symbol. There are arguments to be made in favor of compact symbols the size of a single character, but that's a matter of fine arts or industrial design more than linguistics.
Relatedly one could ask for the optimal size of a languages character inventory and compare e.g. the mess that is the Chinese logogram-syllabary potpourri.
Corollary: If the name is arbitrary, then the symbol may be, too. Thus there can't be one correct answer to your question.
In many ways tradition trumps ergonomics; At least one might argue that linguistics is more adapt at describing what-is, not inventing what-could-be.
You might want to take a look at APL, the obfuscating programming language, for a heavy use of single-character-width identifiers and operators. It still shows numbers written out. That's the most common depiction of numbers we know. In essence, we describe numbers by the computation that derives them, so any computable number can be identified by a function that produces the number.
The lowest decimal numbers are a different matter. The arabic numerals have been developed over millenniums for optimal legibility. There is no need to reinvent them. The smallest ones are even homologic (or ideographic), 1 is one stroke, 2 is two and so on. And zero was for a long time not written at all. This reminds of the integration of counting into the visual cortex. Few other things are integrated as deep, that would require mathematical symbolism and could make use of it at the same time. Audible symbolism may rely to a degree on the auditory portions of the brain. Letters that describe the phonetics of the word somewhat marry both ideas. You'd be hard pressed to find other graphemes that imply the sound of pie. Since maths is for better or worse still taught mainly auditory, or discovered in non-symbolic ways, the need for intricate symbol design is just not there, I guess.