Technology

This is Not a Trig Function

I spend a lot of time looking at New York State Math Regents Exams.  In addition to the critical analysis of the exams I undertake here, we typically grade several thousand exams at the end of each year at my school.

When grading so many exams, it’s not uncommon to feel disoriented and unsettled looking at the same problems over and over again.  However, there was something particularly unsettling about this question.

This trigonometric function just appeared to be too round to me.  Perhaps my senses were just dulled after hours of grading.

Thankfully, we have Geogebra to settle such mathematical disputes.

I was right!  It is too round.  Thanks again, Geogebra, for enabling my mathematical compulsions.

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By patrick honner, ago

Mathblogging.org Profile

Mathblogging.org is running a series of profiles of math bloggers called Mathematical Instruments, and I am happy to be their latest subject.  You can learn a little bit more about me and my blogging history here:

http://mathblogging.wordpress.com/2012/10/20/mr-honner/

Mathblogging.org has played a significant role in my development as a math blogger, so I am quite proud to be a part of this series.

Around the time I started putting together my website, Mathblogging.org came into existence.  Mathblogging instantly connected me to dozens (and ultimately, hundreds) of other math bloggers from the worlds of academia, industry, and education.  It was a place for me to see what different people were writing about and where the conversations were happening.  I felt an immediate sense of community, which made my own blogging seem more relevant.

And I was always excited and proud to make Mathblogging’s Weekly Picks.  It gave me a sense that people were actually reading, and enjoying, what I was publishing.  That positive feedback encouraged me to continue writing about math, taking mathematical photographs, and reflecting about what I could share with the greater math and education community.

So happy birthday to Mathblogging.org!  Thank you for connecting me to so many fascinating and inspiring people, and for helping me find my place in the math blogging community.

By MrHonner, ago

Ancient Lego Robotics

The antikythera machine is commonly referred to as the “world’s oldest computer”.  Dating back to around 150 B.C., the mechanism was discovered in a shipwreck around 1900, and it has amazed scientists and engineers with its precision craftsmanship.  Recent x-ray analyses of the object helped bolster the conclusion that it was designed to predict eclipses, and probably was able to do so with remarkable accuracy.

What could be more amazing than a 2000 year old computer?  Perhaps this working replica of it, made entirely out of legos.

https://www.newscientist.com/blogs/nstv/2010/12/worlds-oldest-computer-recreated-in-lego.html

This video shows the functioning lego replica and gives some of the mathematical background relevant to how the machine operates (apparently the ratio 5/19  is extremely important for calculating the cycles of ellipses) .  Throughout the video, the machine is deconsrtucted and you can see the inner-workings of the various parts.  Truly amazing.

By patrick honner, ago

Cool Graphs of Implicit Relations

This is a cool collection of graphs of relations using software called GrafEq:

http://www.xamuel.com/graphs-of-implicit-equations/

For example, at the right is the graph of

e^{sinx + cosy} = sin(e^{x+y}).

There are several other cool graphs displayed here.

It is worth noting that Wolfram Alpha can graph these relations, too.  For example, here is the above equation:; while Wolfram Alpha captures the spirit of the graph, the image is not as detailed or attractive as the GrafEq version.

By patrick honner, ago
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