Welcome to the 34^{th} Carnival of Mathematics!

There are 34 musicians who have performed as members of Deep Purple or Rainbow [Ritchie Blackmore is notorious for his personnel changes.]. And on the subject of music, Maria Andersen from the Teaching College Math Technology Blog submitted the song “How Do you Write Your Math in Online Classes” (sung to the tune of “How do you solve a problem like Maria”), complete with Listen Now.

There are 34 islands in the Mediterranean (according to Wikipedia). One of the islands is Samos, where Pythagoras was born. And in An Ancient Mathematical Crisis, Denise of Let’s Play Math! explains how the proof that √(2) is irrational shook the philosophical world of the Pythagorean Brotherhood.

Two possibly interesting facts about the number 34 are that 34 is the 4th root of 10^{6}+(10^{3}+1)·336, and that 34 is equal to 3^{2}+5^{2}, which makes it the first composite number that is the sum of two nonunit coprime squares. Two absolutely interesting posts were submitted by Julie Rehmeyer from Math Trek: Detangling DNA, which examines the knots that form in DNA, and Insights into Symmetry, which explains a bit more about the math behind this year’s winners of the Abel Prize, awarded this month.

The number 34 is a Fibonacci number. It’s possible to use a 2×2 matrix (and eigenvalues and diagonalization) to find an explicit formula for the Fibonacci numbers. Another thing that can be done with a 2×2 matrix is to take its determinant, and in Determinants as proportions, on Matt-a-matical Thinking, Matt writes about how determinants can be used to solve proportions and why it might be worthwhile to teach proportions that way.

The number 34 can be written as 1/4 + 2/4 + 3/4 + 1 + 5/4 + … + 4 [the sum of all the consecutive quarters up to 4]. To explore consecutive integers rather than consecutive quarters, head over to Math and Logic Play: Adding Up a Consecutive Range of Integers, shared by Praveen at Math and Logic Play.

The number 34 is the smallest natural number N where N-1, N, and N+1 have the same number of factors. The numbers 0 and 1 don’t have the same number of factors, but within the interval [0,1] it’s possible to pick some random numbers and look at the largest one; Barry poses some intriguing questions about this in Random Expectations, posted at fashionablemathematician – mathematics.

Country star Gretchen Wilson just completed her GED at the age of 34. (Contratulations Gretchen!) She had dropped out of school in 9^{th} grade to start work, but if she’d stayed in school her teachers might have given quizzes occasionally. And I’m sure that those teachers would have appreciated having a site to go to for creating tests, as Larry Ferlazzo shares “That Quiz” posted at Larry Ferlazzo’s Websites Of The Day For Teaching ELL, ESL, & EFL.

There were 34 States in the US at the start of the American Civil War. This kind of information is often represented with a map, which is a kind of graphic. And if you’re going to include graphics in any sort of presentation, you would do well to make them accurate and not slyly misrepresent the data. jd2718 shares this exact kind of situation in Lying with graphics at NYCDOE Central.

On average, the amount of time that passes between two people dying of heart diseases in the US is 34 seconds. Even if you didn’t know that (you didn’t know that, did you?) if someone told you the average was -34 seconds, or 10 billion trillion seconds, you’d probably know enough to question their results. A reality check, in other words. Julie Bloss Kelsey, aka Mama Joules, shares her own mathematical anecdote about reality checks and saving money in Always get a reality check.

One last fact is that the STS-34 (the Shuttle Atlantis) took the Galileo space probe into orbit in October 1989; Galileo arrived at Jupiter in 1995, and remained in orbit gathering data on the Jovian system until 2003. And one last contribution is that today, May 30, is the birthday of Karl Feuerbach, as TwoPi shares in Mathematician of the Week: Karl Feuerbach, the third of a new weekly (Sunday) post here on 360.

See you at the next Carnival of Mathematics, on Friday the 13th of June, over at CatSynth!