{"id":9407,"date":"2014-09-11T14:52:13","date_gmt":"2014-09-11T06:52:13","guid":{"rendered":"http:\/\/www.intmath.com\/blog\/?p=9407"},"modified":"2019-07-07T14:58:20","modified_gmt":"2019-07-07T06:58:20","slug":"carnival-of-mathematics-114","status":"publish","type":"post","link":"https:\/\/www.intmath.com\/blog\/mathematics\/carnival-of-mathematics-114-9407","title":{"rendered":"Carnival of Mathematics 114"},"content":{"rendered":"

\"Carnival
\n Helix Bridge and Flyer, Singapore<\/p>\n

114<\/span> is a sphenic <\/strong>number (the product of 3 distinct prime numbers):<\/p>\n

114 = 2 × 3 × 19<\/p>\n

It's also a repdigit<\/strong>: 114 = 2227<\/sub><\/span> (the digits repeat in the base 7 representation) <\/p>\n

It's the 19th number in the Padovan<\/strong> sequence, given by the recurrence relation P<\/em>(n<\/em>) = P<\/em>(n<\/em> − 2) + P<\/em>(n<\/em> − 3)<\/span>, and where the first 3 terms are 1.<\/span><\/p>\n

114 is an abundant number <\/strong>(where the sum of its proper divisors is greater than itself):<\/p>\n

1 + 2 + 3 + 6 + 19 + 38 + 57 > 114<\/p>\n

That's appropriate, as we have abundant posts for this, the 114th Carnival of Mathematics! <\/p>\n

On with the show. <\/p>\n

1. Visual math<\/h2>\n

a. The Spellbinding Mathematical GIFs Of Dave Whyte<\/h3>\n\n\n
\"Animated<\/a><\/td>\nNow here are some animations that could be the basis for some interesting class discussion.
\n See <\/p>\n

The Spellbinding Mathematical GIFs Of Dave Whyte<\/a><\/p>\n<\/td>\n<\/tr>\n<\/table>\n

b. 6th meeting on Origami, Science, Math, and Education<\/h3>\n\n\n
\"Mathematical<\/a><\/td>\n\n

Andrea Hawksley gives us a nice roundup of the recent meeting on Origami, Science Math and Educaion. She features some of her own work, as well as other gems that were presented.<\/p>\n

See: <\/p>\n<\/td>\n<\/tr>\n<\/table>\n

6th meeting on Origami, Science, Math, and Education (6OSME)<\/a><\/p>\n

While you're there, mouse over Andrea's name in the header of her blog. It's cute.<\/p>\n

c. Random Walks Mural<\/h3>\n\n\n
\"Random<\/a><\/td>\n\n

Mike Chase of "Walking Randomly" tells us about producing three 2-dimensional random walks on the back wall of his classroom. There is a video documentary with time lapse footage, and a discussion of some of the math questions that arise when thinking about random walks.<\/p>\n<\/td>\n<\/tr>\n<\/table>\n

That's logical, as it's the name of his blog! See <\/p>\n

Random Walks Mural <\/a><\/p>\n

2. Rants <\/h2>\n

a. BBC Sport's Anti-Smartness Bias<\/h3>\n\n\n
\"BBC<\/a><\/td>\n\n

Colin Beveridge of "Flying Colours Maths" rants against what is all-too common in the media: laughing at the nerds. He argues the case that if we want a culture where science and maths are seen as important things to study, we might start by making sure people who study them aren’t criticised for it.<\/p>\n<\/td>\n<\/tr>\n<\/table>\n

See:<\/p>\n

BBC Sport's Anti-Smartness Bias<\/a><\/p>\n

b. The science at the end of the Whoniverse<\/h3>\n\n\n
\"Dr<\/a><\/td>\n\n

In a similar vein, Gilead of \"Tycho's Nose\" rants about inaccuracies (or part-truths) in background equations as seen in the new Doctor Who series. See: <\/p>\n

The science at the end of the Whoniverse<\/a><\/p>\n<\/td>\n<\/tr>\n<\/table>\n

c. Stem and Leaf – is there a point?<\/h3>\n\n\n
\"Stem-and-leaf<\/a><\/td>\n\n

Here's a rant of a different nature. Stephen Cavadino of "cavmaths" questions whether stem-and-leaf plots are a necessary part of the math curriculum. See: <\/p>\n

Stem and Leaf – is there a point?<\/a> <\/p>\n<\/td>\n<\/tr>\n<\/table>\n

3. Exploring math ideas <\/h2>\n

a. When do n<\/em> and 2n<\/em> have the same digits? <\/h3>\n\n\n
\"Hamiltonian<\/a><\/td>\n\n

Mark Dominus provides us with a neat exploration of numbers that are permutations of each other. His first example is the decimal expansion of n<\/em>\/7.<\/p>\n<\/td>\n<\/tr>\n<\/table>\n

See:<\/p>\n

When do n and 2n have the same digits?<\/a><\/p>\n

b. The Revenge of the Perko Pair<\/h3>\n\n\n
\"Revenge<\/a><\/td>\n\n

Richard Elwes introduces us to an interesting knotty problem. It turns out this generally accepted picture is wrong... See how at:<\/p>\n

The Revenge of the Perko Pair<\/a><\/p>\n<\/td>\n<\/tr>\n<\/table>\n

c. Looking for Life<\/h3>\n\n\n
\"R<\/td>\n\n

Antonio Sánchez Chinchón presents an R implementation of Conway's Game of Life, a cellular automaton that could support universal computation. He looks for periodic objects able to do computations in the Game Of Life. See<\/p>\n

Looking for Life [no longer available]<\/p>\n<\/td>\n<\/tr>\n<\/table>\n

d. When Greedy Algorithms are Perfect: the Matroid<\/h3>\n

\"Greedy<\/a>Jeremy Kun of "Math ∩ Programming" explores optimal greedy algorithms and matroids. <\/p>\n

See:<\/p>\n

When Greedy Algorithms are Perfect: the Matroid<\/a><\/p>\n

e. Arc length of a spiral around a paraboloid<\/h3>\n

\"arc<\/a><\/p>\n

This post, right here on "squareCircleZ", was inspired by a reader's question. He makes solar cookers for use in Africa and wanted to know how to construct the spiral length around his cookers. It's some "real-world" math that involves sustainable, cheap energy.<\/p>\n

See:<\/p>\n

Arc length of a spiral around a paraboloid<\/a><\/p>\n

5. Math history<\/h2>\n

a. Look Ma, No Zero<\/h3>\n\n\n
\n

0 <\/span><\/p>\n<\/td>\n

\n

In a lot to do about nothing, Evelyn Lamb of the Scientific American blog, recounts her journey of discovery with her students, which involved decipering Plimpton, the 4000 year-old Babylonian tablet. <\/p>\n<\/td>\n<\/tr>\n<\/table>\n

So how did the Babylonians work in base 60, without 0 as a place holder?<\/p>\n

See: <\/p>\n

Look Ma, No Zero<\/a><\/p>\n

b. How The Ancient Egyptians (Should Have) Built The Pyramids <\/h3>\n\n\n
\"Pyramid<\/a><\/td>\n\n

So, how did the ancient Egyptians move those 2.4 million blocks, weighing up to 80 tonnes? In this Physics arXiv post, we learn: <\/p>\n

Modifying square blocks to form dodecagons would have made them easy to roll, say physicists.<\/p>\n<\/td>\n<\/tr>\n<\/table>\n

See:<\/p>\n

How The Ancient Egyptians (Should Have) Built The Pyramids<\/a><\/p>\n

6. Plug<\/h2>\n

\"MOOC<\/a>This post is a plug for an experimental MOOC (Massive Open Online Course). The blurb says:<\/p>\n

"Citizen Maths is an online resource anyone can use — to discover how maths can be a powerful tool for solving those problems that come up at work and in your life."<\/p>\n

See: <\/p>\n

Citizen Maths MOOC<\/a> <\/p>\n

7. Reflections<\/h2>\n

\"Reflection\"<\/a>So, what is mathematics? Shecky Riemann of "Math-Frolic" has a quote from How Mathematicians Think<\/em>, by William Byers, which ponders that math is a series of situations where we are led to observe, <\/p>\n

"Something's Going On Here<\/a>" <\/p>\n

8. Final bit<\/h2>\n

I hope you've enjoyed Mathematics Carnival #114, coming to you from Singapore. <\/p>\n

The next carnival will be at MathTuition88<\/a>, slated for October 2014. See where and how to submit<\/a>. <\/p>\n

Image credits: <\/h5>\n

Singapore Helix and Flyer<\/em> by ensogo, accessed from http:\/\/www.ensogo.com.ph\/escapes\/singapore-flyer-cruise-09092012.html<\/p>\n

BBC Sport logo<\/em>, by BBC, accessed from http:\/\/www.bbc.com\/sport\/0\/ <\/p>\n

Stem & leaf plot<\/em> by ck-12.org, accessed from http:\/\/www.ck12.org\/book\/Basic-Probability-and-Statistics-A-Full-Course\/r4\/section\/7.2\/<\/p>\n

Reflection<\/em>, by Marcia Birken, accessed from http:\/\/alumnae.mtholyoke.edu\/blog\/light-motifs-marcia-birkens-images-meld-math-and-art\/<\/p>\n

All other images are from the posts to which they link. If you have any objections to their use in this manner, let me know and I'll remove them. <\/p>\n

See the 5 Comments<\/a> below.<\/p>\n","protected":false},"excerpt":{"rendered":"

\"Carnival<\/a>
\nThe Carnival of Mathematics is a collection of recent math blog articles covering visual math, various rants and some math history, by various authors.<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_mo_disable_npp":""},"categories":[4],"tags":[127],"_links":{"self":[{"href":"https:\/\/www.intmath.com\/blog\/wp-json\/wp\/v2\/posts\/9407"}],"collection":[{"href":"https:\/\/www.intmath.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.intmath.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.intmath.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.intmath.com\/blog\/wp-json\/wp\/v2\/comments?post=9407"}],"version-history":[{"count":2,"href":"https:\/\/www.intmath.com\/blog\/wp-json\/wp\/v2\/posts\/9407\/revisions"}],"predecessor-version":[{"id":12049,"href":"https:\/\/www.intmath.com\/blog\/wp-json\/wp\/v2\/posts\/9407\/revisions\/12049"}],"wp:attachment":[{"href":"https:\/\/www.intmath.com\/blog\/wp-json\/wp\/v2\/media?parent=9407"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.intmath.com\/blog\/wp-json\/wp\/v2\/categories?post=9407"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.intmath.com\/blog\/wp-json\/wp\/v2\/tags?post=9407"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}