Johann Lambert discovered that Pi cannot be expressed as a fraction, implying its digits go on forever.
The question of who "discovered that pi was infinite" is somewhat ambiguous. Pi is not "infinite" in the sense of being infinitely large. Rather, the digits in its decimal representation never end and never repeat. A more accurate question would be: Who proved that pi is an irrational number, meaning it cannot be expressed as a fraction and therefore its decimal representation is non-repeating and non-terminating?
The answer to the revised question is:
Johann Lambert
In 1768, Johann Lambert, a Swiss mathematician, proved that pi is an irrational number. This means that it cannot be expressed as a simple fraction (a/b, where a and b are integers). As a consequence of being irrational, the decimal representation of pi goes on forever without repeating. Lambert demonstrated that it's impossible to find any fraction that exactly equals the value of pi.
Here's a summary of the key points:
- Irrationality: Pi is an irrational number.
- Non-repeating decimal: The digits of pi never repeat in a pattern.
- Non-terminating decimal: The digits of pi go on infinitely.
- Lambert's Proof: Johann Lambert proved the irrationality of pi in 1768.
Therefore, while not "infinite" in the sense of size, Lambert showed that the decimal representation of Pi goes on forever without repeating, a critical step in understanding its nature.
