The Carnival of Mathematics #20

Welcome to the 20th Carnival of Mathematics.

Carnival Ride in a Bubble
Image source

Because this Carnival is coming from Asia, I thought it would be fun to number the submissions using Chinese and Indian numerals.

During the last 3,000 years or so, the Chinese have influenced the way numbers were written in most of Asia, but especially in Japan, Korea, Vietnam and Taiwan. While Western numerals are common-place, Chinese numerals are still in wide use in China and Japan.

The Indian numbering system had a profound influence on mathematical development. Without the Hindu’s base 10 positional system, European countries could still be using Roman numerals. The Arabs (especially al-Khwarizmi in the 9th century CE) promoted the "Indian System" and contributed greatly to its widespread adoption by the West through the 12th century CE. Hence we have the Hindu-Arabic number system.

Depending on your browser and existing fonts, hopefully you are seeing Chinese & Devanagari (Hindi) characters, and not splodges. I have included binary equivalents if you need a translation 🙂 .

On to the Carnival.

一 (0001₂) १

Charles Daney has an interesting analysis of the Uniqueness of factorization.

His blog is Science and Reason.

二 (0010₂) २

In 10 ways to get wild about Math, from blogger Sol Lederman, there is a good list of suggestions for math students (and instructors) covering learning styles, math anxiety and time management.

His blog is enthusiastically called Wild About Math.

三 (0011₂) ३

Alec Klein Interview - The Final Chapter comes from Dave Marain’s MathNotations blog.

Dave says: The last part of the interview with Alec Klein, the author of the critically acclaimed book, A Class Apart, which spotlights the lives of students, teachers and the culture of one of the legendary specialized schools for gifted math-science students, Stuyvesant HS in NYC. Issues of the needs of the gifted and talented are highlighted and don’t miss the comments.

四 (0100₂) ४

Andy Schmitz (who is a high school senior) in LardBucket presents us with an analysis of A Flaw in Shamir’s Secret Sharing method? He invites readers to critique his logic.

Andy is demonstrating some great skills for a future mathematician (eg willingness to chew over some extra-curricular math in his own time, analytical skills, blog skills using LATEX, etc.)

五 (0101₂) ५

Middle Schoolers and the Unsummables is from MathMom. It shows how she used Dave Marain’s Unsummables Activity with a group of young middle schoolers, who rose to the occasion and found lots of great conjectures about the patterns they discovered in the way numbers can (and can’t!) be expressed as the sum of a sequence of consecutive positive integers.

六­ (0110₂) ६

Matlab has a nice colorbar scale for 3D graphs but Mathematica does not. Mike Croucher and a friend sat down and came up with a package that addresses the omission: Mathematica version of colorbar.

Walking Randomly is a nicely formatted blog.

七 (0111₂) ७­

Radu Grigore is next with Optimal alphabetic binary trees. The problem arises from the desire to reduce "dead code" in Java programming.

Radu’s blog is called RGrig’s blog.

八 (1000₂) ८

Vlorbik, in On Finally Teaching Calc II At Long Last, luxuriates over the joys of teaching a group of students who are ’into it’. It is an interesting set of reflections on what most math educators hope to do, at least at some point in their career — teach at a level that is personally challenging, with a class that has students who actually want to be there.

九 (1001₂) ९

Determinants are the focus at Matt’s Matt-amatical Thinking (ya gotta love that blog name).

His post, Determinants are calling me..., has a nice description where his class is given space to explore mathematics, rather than just listen to it. The lesson starts with a question and this triggers some great ’teachable moments.’

十 (1010₂) १०

From Let’s Play Math, Denise challenges educators to come up with good explanations for middle school fraction FAQs in Quiz: Those frustrating fractions

How would you explain the mistakes to a struggling math student?

十一 (1011₂) ११

Meep (aka Mary) is starting a YouTube series called Meep’s Math Matters. The series will consist of short videos on basic/classic math concepts.

She talks about triangular numbers in the first video and requests suggestions for future videos.

十二 (1100₂) १२

My contribution for Carnival 二十 is about Web user data in CrazyEgg Web Analytics, right here in squareCircleZ.

We are being watched...

十三 (1101₂) १३

Jonathan rants about New York Sample Algebra Questions in his jd2718 blog. His commentary is on a newly designed standardized exam.

His conclusion: ’It’s a lousy exam’.

十四 (1110₂) १४

And for an interesting contrast to Jonathan’s New York exam blues, we move to Singapore.

Miss Loi runs Jφss Sticks. This visually-rich and popular blog includes PSLE 1 Higher Education 0.

Singaporeans just love acronyms, so let me give you a heads-up: ’PSLE’ is Primary School Leaving Examination, ’JC’ = Junior College (16 & 17 year-old, pre-university), Secondary One (13 yr old, Grade 7), E-maths (taken by O-Level, or grade 10 students). The bookstores in Singapore are amazing - they consist of shelves full of ’assessment books’, which are exam papers from previous years.

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So that’s it - I hope you enjoyed Carnival of Mathematics #20.

Endpiece #1: Don’t you hate it when you are listening to someone who mumbles and they are trying to say the number ’15’. How often do you have to ask such people if they said ’fifty’ or ’fifteen’? In spoken Japanese (and Chinese, of course), there is a clear distinction between 五十 ’go juu’ (50) and 十五 ’juu go’ (15).

Endpiece #2: And since we started with a quick explanation of Asian number systems, here is a video where you can learn Japanese numbers. I’m making it this week’s Friday Math Movie:

See previous Friday Math Movies.

See the 11 Comments below.