August 26 – Happy Birthday, Johann Heinrich Lambert

Posted on August 26, 2014

You know how we love celebrating Pi Day every March 14? Well, today we can eat pie again—this time, birthday pie in honor of the fellow who proved that pi is an irrational number!

Johann Heinrich Lambert, born on this date in 1728, was a Swiss mathematician, physicist, philosopher, and astronomer.

Lambert did a lot of cool stuff in math, including working with non-Euclidean geometry...that is, the kind of geometry that deals with curved space. He also studied conic sections and helped make the calculation of the orbits of comets simpler.

Lambert also studied map projections and showed that map makers could not get BOTH the outlines of landforms AND the size (or area) of those landforms right, because the Earth is round (almost spherical) and maps are flat (pretty much two-dimensional).

In physics, Lambert studied light and perspective and optics and color. In astronomy, Lambert developed theories about the generation of the universe and about star systems. He wrote about logic and philosophy, and he worked with famous philosopher Immanuel Kant.

But pi...ah, pi!

Let's talk about pi!

What does it mean to say that pi is an irrational number?

Rational numbers are those that can be expressed as a fraction. The number 124 is rational because it can be expressed as a fraction:


One-half is rational because it can be expressed as a fraction:


But pi cannot be expressed as a fraction. You may remember that pi is the answer to the problem of dividing a circle's circumference by its diameter. EVERY SINGLE CIRCLE – no matter what it's circumference and diameter – when you divide the former by the latter, you come up with the same exact number....a number that cannot be expressed as a fraction.

(Pi is close to 22/7 – but close is not the same as equal, in math.)

Another way of talking about rational and irrational numbers is to explain that a rational number can be expressed as a decimal, such as these decimal numbers:

8 (which is the same as 8.0)

Some rational numbers are not as simple as these, and they can be represented by decimal numbers that NEVER END but instead go on and on and on and on forever.

Here is one:


This rational number, one-third, can be represented by this decimal number:


EXCEPT to make it accurate, I would have to keep typing 3s forever, and you would have to keep reading 3s forever, and neither of us would get anything else done. Since that would be boring, we call these decimals that go on forever “repeating decimals.” And we write repeating decimals by either:

  1. putting three dots after the part that repeats,
  2. or putting a little line over the top of the part of the decimal that repeats forever.

Here are some more repeating decimals:

Now...that's all rational numbers.
What about irrational numbers?

When you try to show an irrational number as a decimal number, the numbers go on and on forever BUT DON'T REPEAT!

Here is a little bit of pi:

Mathematicians have used computers to figure out the digits of pie out to more than 10 trillion digits! And there is no repeating pattern. We can say that pi is sorta kinda close to 3.14 – but remember, in math “close” is not the same as “equal.”

Today's birthday boy, Lambert, is the first mathematician to offer a mathematical proof that, no matter how far into pi you go, there will never be repeating decimals. In other words, he proved that the number is irrational.

Also on this date:

Women's Equality Day here...

...and here

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