Ingenium Blog

In the last post, we saw that if you take a right triangle with legs of length 1 and 1, the Pythagorean theorem results in: $$ 1^2 + 1^2 = c^2 \rightarrow c^2 =2 \rightarrow c = \sqrt{2} $$ The sum of the area of two squares whose sides are the two legs (blue and red) is equal to the area of the square whose side is the hypotenuse (purple). So the hypotenuse is $\sqrt{2}$. Easy enough, right? Usually in math class we would type this into our calculator aaand we are done. But then still one issue remains… What on earth is $\sqrt{2}$? Based on the fact that $c^2=2>1$ means that it should at least be larger than $1$, but what is it exactly? It does not seem to be a whole number. Which number squared gives $2$? Is it a fraction? Can it be written as one? Just typing this into our calculator doesn’t seem to clear out this issue right? Apparently it was very difficult for ancient civilizations to get around this problem of not finding the exact value of $\sqrt{2...

I really wanted to create this account because way too often the science and math are experienced as intimidating, boring, or even traumatic. For some, math was forced through school. For others, it felt like a constant struggle. The truth is simply that this picture of math is fake 😭. Actually, math and science is playful. You can solve puzzles, find patterns, and discover intriguing results. It is often a story of wrestling with confusion and then feeling the joy of figuring something out. It’s about seeing the invisible structures that shape our universe. Using math you can explain how artificial intelligence works, or how planets move, how water flows or how a plane flies. 🔥 I was lucky to have had very inspiring teachers which presented science as an intriguing discipline. I want this account to be an inspiration for the people wanting to dip in their toes into the world of science and sometimes go even deeper. Life does not always have to be serious so we'll do it here ...

Let’s start with something everyone has at least seen once: the Pythagorean theorem. The theorem shows that in a right triangle, the square built on the longest side, also known as the hypotenuse, is exactly equal to the sum of the squares built on the other two sides. In other words, $a^2 + b^2 = c^2$. The sum of the area of two squares whose sides are the two legs (blue and red) is equal to the area of the square whose side is the hypotenuse (purple). It is an infamous topic in every high school classroom. In addition, it is very common that someone asks “Why does this matter?” or something along the lines of “When will I ever use this in real life?”. Let’s rewind a bit. The Pythagorean theorem is one of the oldest and most famous ideas in all of mathematics. Actually while doing a lot of science, the Pythagorean theorem is an elementary piece of math. In engineering, it becomes so obvious that you don't even think about it anymore. That's how com...