In the history of mathematics there are key moments that marked a before and an after. One of them is Tales of Miletus, a 6th century Greek philosopher, astronomer and mathematician. To him we owe one of the first formalized geometric theorems: the Theorem of Tales, a powerful tool that relates parallelism with proportionality.
What's so special about it? I'll explain later!
First, A little of history to situate us
Thales lived in Miletus, in present-day Turkey. Not only was he the first to seek rational explanations for natural phenomena, but he also pioneered the application of mathematical logic to real problems. One of his most memorable feats is the following:
Tales measured the height of the Great Pyramid of Egypt using his shadow.
How did he do it? He waited for the time of day when the length of his own shadow matched his height. At that moment, the proportions between his figure and the pyramid were equivalent, and he was able to apply a geometric reasoning that we know today as the Theorem of Tales.
What exactly does the Theorem of Tales say?
There are several formulations of the theorem, but one of the best known (and useful)
is the following:
- If we draw several parallel lines that cut into two secant lines, then the segments formed on one line have the same proportion as those formed on the other.
In other words:
If the lines are parallel, the divisions between the generated segments are proportional.
Applications of the Such Theorem in everyday life
Despite its age, this theorem is still valid in many applications. Look at all that can be done thanks to it!
- Construction: Used to ensure that structures are proportionate and symmetrical.
- To measure inaccessible distances using proportions.
- Industrial design: Applied to scale prototypes to life size.
- Photography: Helps to maintain the ratio between objects when composing an image.
Why is it used so much?
The Such Theorem is key because it allows to calculate lengths and heights without having to measure them directly. Thanks to the proportions, data can be derived in a precise and practical way.
Here I leave you a small infographic that I have designed to see more visually the applications of The Theorem of Thales in everyday life.
Why is it so important?
- Allows solving problems without the need to measure directly.
- It is the basis for projective geometry and trigonometry.
- Used in technical drawing, architecture, graphic design, photography, cartography...
- It also appears in modern tools such as computer vision and 3D simulations.
Curiosities
- Such was the first mathematician to prove a theorem, not just to state it.
- Many ancient civilizations measured heights with shadows, but only Tales proved this mathematically.
- Can be applied to check whether two objects are visually proportional.
With this video you will be able to remember the concepts that we have seen in this post.
And that's it for today. I hope you've learned something new and that geometry proves useful in your daily life.
See you in the next geometric adventure!馃З
Bye!
References:
Primaria, M. (2021). Teorema de Thales. Mundo Primaria. https://www.mundoprimaria.com/recursos-matematicas/teorema-de-thales
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