Depending on the order in which these limits are taken, you can get either $4$ or $\pi$. In answer to the following question: However, a layman would ask "why is your strange 'polygonal approximation' method correct, but the π=4 proof's method incorrect?"

Jan 11, 2011 · There is a very simple way to prove whether pi is 4 or not. It is not a very technical experiment, although it is scientific (since science requires observation, and it is readily observable.) Measure the diameter of a cup you have around the house. Let’s say the diameter is …

Aug 9, 2015 · One can use this method of infinite cylinders to prove the volume of a sphere, but when I tried almost the exact same thing for surface area, I found that the value of pi is 4. I have only heard of one other strange proof that leads to this …

Dec 3, 2010 · Summary: The construction at the top (pi=4) merely shows an upper bound. It's an upper bound but it is very easy to come up with a lower but still upper bound to the circumference. The =?4 construction doesn't prove or disprove very much more about the length of the circle besides providing an upper bound pi<4. It certainly doesn't prove =4.

The troll pi meme essentially says: the perimeter at every step is 4, and when we take the limit we get a circle, so the perimeter of the circle is 4. Perimeter is a function: it takes a geometric shape as input, and gives you a number as output.

Mar 10, 2011 · Since the jagged curve gets closer and closer to the circle and always has length 4 we can see that the perimeter of the circle has length 4. But the perimeter length is also equal to π. Therefore, π is 4.

1 day ago · "Using calculus with complex numbers, you can prove π is transcendental," Conrad said. "The proof uses the very famous equation called Euler's identity: e iπ +1 = 0.". Although pi's universal ...

5 days ago · What are some of your favorite fun facts about pi? While in secondary school, teachers usually teach students that an approximation for pi is 22/7, but this approximation is greater than pi. The first four digits of pi are 3.141, while the first four digits of 22/7 are 3.142. Due to misguided approximations like this, the state of Indiana made ...

22 hours ago · Pi, of course, symbolizes the ratio of a circle's circumference to its diameter and equals 3.14 (which is why its celebrated on March 14). The exact value of pi can't be calculated, but that doesn ...

In the 1760s, Johann Heinrich Lambert was the first to prove that the number π is irrational, meaning it cannot be expressed as a fraction , where and are both integers. In the 19th century, Charles Hermite found a proof that requires no prerequisite knowledge beyond basic calculus.