How to Use Wolfram Alpha Inside Google Docs
Wolfram Alpha is a search engine that is probably best know for helping students solve mathematics problems. But there is more to Wolfram Alpha than just computational data. Wolfram Alpha can help students quickly locate information about famous people in history, locate socioeconomic data, find science data, and even help students find information about music theory. Unlike on Google or Bing, when students search on Wolfram Alpha they won't be shown a list of links.

The Harmonious Mathematics of Music
According to legend, the Ancient Greek Pythagoras was once walking on the streets of Samos, when the sounds of blacksmiths’ hammering suddenly gave him an epiphany. Pythagoras rushed into the shop and, as he analyzed mathematically the shapes of the blacksmiths’ hammers, he laid the foundations of music that today’s Rihanna, Shakira and others are building upon. Wait a minute… Are you talking about the guy from the Pythagorean theorem? I am. And despite what you’ve learned at school, this Pythagorean theorem is absolutely not Pythagoras’ greatest idea — most notably because he probably wasn’t even the one who came up with the Pythagorean theorem. At least, that’s what I think: Pythagoras’ greatest idea was the mathematization of music, whose harmonious structures would later be the playground of the greatest musicians like Ludwig van Beethoven (we’ll get there!)

from Wolfram MathWorld
A special function which is given by the logarithmic derivative of the gamma function (or, depending on the definition, the logarithmic derivative of the factorial). Because of this ambiguity, two different notations are sometimes (but not always) used, with defined as the logarithmic derivative of the gamma function , and defined as the logarithmic derivative of the factorial function. The two are connected by the relationship
Math Manipulatives: About Virtual Manipulatives
Math Manipulatives contains three pages of resources: About Virtual Manipulatives What is a virtual manipulative? In What are Virtual Manipulatives?

Fibonacci GCD's, please
Fibonacci numbers exhibit striking patterns. Here's one that may not be so obvious, but is striking when you see it. Recall the Fibonacci numbers:
A Random Math Fun Fact!
From the Fun Fact files, here is a Random Fun Fact, at the Advanced level: The traditional proof that the square root of 2 is irrational (attributed to Pythagoras) depends on understanding facts about the divisibility of the integers. (It is often covered in calculus courses and begins by assuming Sqrt[2]=x/y where x/y is in smallest terms, then concludes that both x and y are even, a contradiction. See the Hardy and Wright reference.) But the proof we're about to see (from the Landau reference) requires only an understanding of the ordering of the real numbers! Proof.
moving-to-math-2-0
" Moving to Math 2.0" Katerina Atmatzidou Math teacher, Greece Learning Diary

Sums of Two Squares Ways
In the Fun Fact Sums of Two Squares, we've seen which numbers can be written as the sum of two squares. For instance, 11 cannot, but 13 can (as 32+22). A related question, with a surprising answer, is: on average, how many ways can a number can be written as the sum of two squares?
Mystery Mathematics in Nature and Universe - Web Education
Mystery Mathematics : The theory can be considered a form of Pythagoreanism or Platonism in that it posits the existence of mathematical entities; a form of mathematical monism in that it denies that anything exists except mathematical objects; and a formal expression of ontic structural realism. There is debate going on among scientists today about whether math discovered or invented by humans, where some believe that mathematics is the hidden language of the universe Others believe that mathematics is the invention enables intelligent human beings in it to predict what is happening in the universe. Einstein’s questions about: How is it possible to be able to interpret the mathematics of the universe is a good way that we see it Are we discover or invent mathematics ??? From time immemorial, man in search of cycles and patterns, used them to explore the physical world and to understand the rules of nature, the number of flower petals (answering “suites”) symmetry of our body. other item

Odd Numbers in Pascal's Triangle
Pascal's Triangle has many surprising patterns and properties. For instance, we can ask: "how many odd numbers are in row N of Pascal's Triangle?" For rows 0, 1, ..., 20, we count: row N: 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 odd #s: 1 2 2 4 2 4 4 8 2 4 04 08 04 08 08 16 02 04 04 08 04
10 Unusual Ways to Explore Math
I confess. I never really liked math. I played the school game well so I received pretty good grades, but after I passed the test (even after receiving an A in most cases), those rules, theorems and facts didn’t stick around for very long. The problem was everything was drilled into me, or as I like to think now, drilled out of me. I sat and did problem after problem before I really had a great grasp of with math could mean, how it related to my life and how I could approach it in a way that made sense to me. Everyone is different, but I needed more hands-on things, more time to invent my own problems.

Music Math Harmony
It is a remarkable(!) coincidence that 27/12 is very close to 3/2.