Last week I published an article on **60 Stunning Satellite Images of Earth**. I am a push-over for interesting and surprising images and photographs. This week I was fascinated by the original blueprints for the Eiffel Tower. Click on the image below to see the official Eiffel Tower site and the blueprints (or click here.)

**Two points:**

- I find them intriguing visually. Even beautiful.
- I am amazed that this information is available to me through the web. (What are the chances that I would have come across that 15 years ago, unless I was an architect?)

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Hello Will

I have a bit of an ice breaker for you about the Eiffel Tower. Do you know how Gustave Eiffel originally came up with the

idea of how to construct the base of the tower?

Will,

I wouldn’t have thought that the original blueprints of the Eiffel Tower would be available online. But I suppose I shouldn’t be surprised since it seems like the Internet these days has almost anything available you can think of.

I’m no engineer or architect, but I’m a mathematician, and mathematicians generally do appreciate structure and beauty because there is plenty of that throughout mathematics. For example, groups, rings, fields, vector spaces, etc. are sets of objects with some structure defined on them. One of the most beautiful and elegant proofs in mathematics is Euclid’s proof that there are infinitely many prime numbers.

Besides groups, rings, fields, etc., we see structure in math in the logic and development of mathematical theories, regardless of what theory it is.

These blueprints do contain many details (overwhelmingly many, especially if you’re not familiar with them), but detail is important if architects or engineers want to build a stable structure. That reminds me of the vitality of details in mathematics. Even one minor detail that is off a bit can cause a proof or derivation to collapse on you! Students can sometimes get a bit irritated by us math teachers when it comes to detail, but details cannot be ignored in mathematics! Those who succeed in mathematics are sensitive to details.

Speaking of mathematics, I’m sure a lot of math had to go into the design and construction of the Eiffel Tower. I wonder where the Golden Ratio arises in this construction since the Golden Ratio arises in plenty of things. The Golden Ratio arises in unexpected places; for example, the formula for the n-th term of the Fibonacci sequence uses the Golden Ratio. There’s some beauty right there!

One of the most beautiful things about mathematics is that the theorems in math never go out of date. Scientific theories come and go, but mathematics developed centuries or millenia ago are just as true today as back then. The Eiffel Tower is lovely, but it won’t stand forever. The theorem that there are infinitely many prime numbers will stand forever!

Jonathan Groves

KU Math Faculty