Math Vs Baking

Hello everyone! As you may know from my earlier blogs, I am a Mathematics major who enjoys the world of baking. Thus, in this blog, I would like to share how they both intertwine. Specifically, I would like to share how the Thales Theorem has improved my baking skills.

We all had our fair share of temporary COVID hobbies. Mine was baking, yet this little hobby was not temporary. As my love of baking did root from a viral spread, it started out as just making baked goods for friends and family. As my skills started to progress, there was a demand for my sweet treats from complete strangers who then turned into lovely returning customers! This is why I chose this topic. Baking is something that I do weekly, and it is one hobby that is extremely common. Looking into mathematical ideas such as the Thales Theorem, Newton's Law of Cooling, and the Binomial theorem will help us improve our baking skills. Now the question is, how?

Let us take a dive into the beautiful world of ratios. Specifically, the Basic Proportionality Theorem, which is also known as Thales Theorem. This theorem was named after the Greek Mathematician Thales of Miletus. According to the article "The Theorem of Thales: A Study of the Naming of Theorems in School Geometry Textbooks, "Thales calculated the distance toe points by applying the theorem, the inaccessible which states that two triangles are equal when one of their sides and two adjacent angles are equal." Thus, based on this concept, when looking at two similar triangles, we know that the consistent sides of both of those triangles are proportionate to each other. This includes even if the triangles were to be scaled.

As mentioned, I do bake very often for people, and one thing that I always like to ask myself is, "How can I enhance this recipe?" As many may know, ratios play an important role in Baking. A few weeks ago, I had an order for one full tray of brownies. Now, this was only going to be my second time making a batch of brownies. The first time that I attempted to make brownies they were personally not up to par. Don't get me wrong, they were very tasty, yet, I wanted them to be more fluffy as well as more fudgy. The brownie recipe called for one stick of butter. What some may not know is that butter allows brownies to become more soft and fudgy. Thus, I up-scaled the ingredient to two sticks of butter instead of one. Because I up-scaled the butter, I had to upscale the amount of vanilla extract and chocolate chunks so we could balance out that "buttery" taste that we would have had due to the extra butter that was added.

As suggested earlier, when looking at two segments that are proportionate to each other, when they are scaled, they remain proportionate. Because I up-scaled the amount of chocolate chunks and vanilla to balance out the butter, it allowed the brownies to remain intact and in balance. Now, let us take a look at an actual example of Thales' Theorem. Say that there exists a triangle SHA. If line GO is parallel to HA and intersects both sides, SH and SA at the points G and O, then SG/GH is equivalent to SO/OA. As we see, the segments SG and GH on the side of SH, are proportional to the segments SO and OA on the side of SA. Within this example, we see that the segments in triangle SHA maintain their proportionality. In baking, just like my brownies, the ratios of the ingredients must also be adjusted to maintain that overall balance.

In essence, manipulating ratios and proportions is the root of Thales' Theorem as well as baking. Within the segments of triangle SHA, we see that they maintain their proportion when scaled, just like the ingredients in a recipe, so they can achieve that perfect balance. I was able to improve the brownie recipe by using these ideas! Please take a look at the figure 1 and 2 below, the effect of scaling ratio to maintain balance as implied by Thales Theorem, in the form of brownies!

Figure 1

Figure 2

Well, I hope you enjoyed this educational text! Until next time, Shada :)