Synopsis:

The expression: \( \frac{\pi}{t} \cdot p \), which simplifies to \( \frac{\pi \cdot p}{t} \).

Yields the following three dimensional plot:

Source: https://www.wolframalpha.com/input?i=%5Cfrac%7B%5Cpi%7D%7Bt%7D+%5Ccdot+p+

Observations:

• The \( \pi \) constant does the heavy work* by being put in the numerator of the expression.
• Assuming only that \( \pi \cdot p > t \), there exists an interval of reals where the three dimensional plot becomes degenerate.

Notes:

[1] work*: By being factored as a numerator and being nth times greater than t per the assumption \( \pi \cdot p > t \), this explains the behavior on the three dimensional plot.