The Palace of Discovery *(Palais de la Découverte)* is a science museum located in the west wing of the *Grand Palais*, in the 8^{th} arrondissement of Paris. The museum was founded in 1937, and in 2010 it was merged, for administrative purposes, with the larger Sciences and Industry Museum *(Cité des sciences et de l’industrie)* over in the *Parc de la Villette* in the far northeast corner of Paris. So the two museums are now under the same management, and the joint institution is known officially as *“universcience”*.

In 2016 the museum celebrated the hundredth anniversary of Einstein’s theory of General Relativity with a temporary exhibit consisting mainly of text panels, in French and English, explaining in laymen’s terms how Einstein developed the theory and how it was later proven to be true. Apparently we all prove it every time we use the Global Positioning System (GPS) to determine our position on the surface of the earth. Since GPS depends on satellites circling the earth at an altitude of twenty thousand km, the system has to correct for the fact that, as Einstein predicted, time moves a tiny bit more slowly up there than it does down on Earth. (Or is it the other way around? In any case, the system wouldn’t work if it didn’t correct for relativistic effects.)

As a non-mathematician I tend to be astounded at things that any self-respecting mathematician no doubt finds self-evident. One of these is *π* (or *pi*), the ratio of a circle’s circumference to its diameter. So I was pleased to see that the museum has an entire room devoted to *π*. Appropriately, the room has the form of a circle, and around the inside walls they have printed the value of *π* to a precision of 707 decimal places, which is only a small fraction of the decimal places that have been worked out to date, but a much greater precision than is needed for most practical purposes. In high school we were satisfied with 3.1416, which was already more precision than our slide rules could handle.

Above the entrance to the *π* room is an equation which I first took to be the mathematicial equivalent of “Abandon all hope, ye who enter here”, but which I soon learned was “Euler’s Identity”:

**e ^{iπ} + 1 = 0**

In the text panels, various people are quoted as saying that this is “most beautiful theorem in mathematics” and that it is “absolutely paradoxical; we cannot understand it, and we don’t know what it means, but we have proved it, and therefore we know it must be the truth.” The letter *e* in the formula is “Euler’s number” (roughly 2.718281828…), which when raised to the power of *iπ* (*i* being the imaginary number representing the square root of minus one, which does not exist and is a logical impossibility) is equal to -1.

While trying to imagine how any number could be raised to the power of *iπ *(multiply it by itself *iπ-1 *times, whatever that means), I was reminded of a novel I once read in German called *Die Verwirrungen des Zöglings Törleß* (The Confusions of Young Törless) by Robert Musil (1880-1942). Among all his other confusions, the protagonist Törless fears he is losing his grip on reality when he tries to get his head around the concept of imaginary numbers, which are as important as they are impossible.

Speaking of slide rules, I was happy to see one bolted to one of the tables. I set it to 2 before taking the photo, so you can see that 2 times 2.75 equals 5.5, for example, or 2 times 2750 equals 5500, or two times 275000 equals 550000. The catch was that the slide rule could show you the result but not the order of magnitude, which was the downfall of many a high school student in those days.

Mathematics, science and engineering were basically all done with slide rules throughout the seventeenth, eighteenth and nineteenth centuries and the first six decades of the twentieth century. Then in 1972 Hewlett Packard came out with the first handheld calculator, and by 1975 slide rules were a thing of the past.

Even earlier, when IBM first starting advertising their mainframe computers in the 1950s or 60s, they claimed one of their computers could replace 720 engineers using slide rules — which was probably true, but only the largest companies could afford a mainframe computer.

On his website http://www.sliderule.ca/ (which I am happy to see is still online) Eric R. Marcotte wrote: “In the history of the modern world, probably no other technological instrument was so widely used for so long, only to disappear virtually overnight.”

To find out more about slide rules, try Ron Manley’s Slide Rule site or the virtual international Slide Rule Museum, or look up the article “When Slide Rules Ruled” in the May 2006 issue of *Scientific American*.

When I was in high school the real math freaks used to wear 36-inch slide rules in a scabbard on their belts, like a sword. I wasn’t in that league, but I always had my normal 12-inch slide rule with me. I still have two or three slide rules around the house somewhere, but haven’t used them for years since a 5-Euro pocket calculator can now achieve the same (or better) results.

*My photos in this post are from 2016. I revised the text in 2017.*

The Grand Palais is on the Avenue Franklin Delano Roosevelt, 75008 Paris.

Location on the Vélib’ map.

Location, aerial view and photo on monumentum.fr.

clever idea that circled-shaped π room!

Very interesting review. While calculators had indeed just come out in the mid seventies I was still requird to buy a slide rule for my first year in high school (74/75 if memory serves me rightly) At first calculators were banned but very quickly accepted. I think we were the last year that was required to have a slide rule.

I never used a slide rule in school! Then I didn’t take any advanced math, so maybe that’s why. Interesting tour! Thanks Don!