A blog about Mathematics and Mathematics Education in Singapore, as well as Mathematics Education in general. Written for students, parents, educators and other stakeholders in Singapore, and around the world.
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Summary
Although the concept of "transcendental number" was not defined during Newton's time, Newton's Principia contained the germ of idea that seems to lead to a relatively easy proof of the idea that p is transcendental. Arnol'd described how Newton showed that the trajectory of planets cannot be expressed in terms of any polynomial function of time.

It looks
like some pediatrician
is complaining that maths (that's the way we spell it in Singapore) is
too hard.

Paul has two-thirds as many postcards as Sean has and the
number of postcards Sean has is three-fifths the number of postcards Tim has.
If the boys have a total of 280 postcards, then how many more postcards does
Tim have than Paul?

He says “Obviously it’s complex, but not impossible, ... I would use a complex algebra equation to solve it and I’d
guess it’s more appropriate for an eighth and ninth grade student than one
still in thefifth grade.”

Oh really? Here's an easy solution. No
complicated ("complex" can mean a few other things) algebra, nor
any algebra for that matter is needed.

To answer the question "Do pediatricians suck at
maths?" My answer is: I don’t know.

This is an interesting piece of inspirational waffle about p to celebrate "p day". Hopefully this special day helps to keep this important piece of knowledge that has a long cultural history fresh in our collective human consciousness, and perhaps stem the decline in mathematical literacy of some of us.

However, his article made me wonder whether he knew what transcendental means. It is a pretty technical concept, and even if one knew what it means, it's a challenge to put it in layman's terms and say something funny with it. If he knew the meaning, he certainly did not show it.

My Comments
This is a well-produced video in which the team took great care in producing an interesting narrative. The circles were drawn imperfect and shaky, so as to catch the attention of viewers and to highlight them. A couple of points they missed out:-

1) p being irrational, does not only have an infinite number of digits in its decimal expansion, the digits are also non-repeating. A rational number (fraction) like 1/7 also has an infinite number of digits, but they repeat: 1/7 = 0.142857 142857 142857 ...

2) near the end of the video, the animators depicted universe < p. I find the artistic licence disturbing. I am sure there is some way to artistically depict the known universe having less number of atoms than number of digits of p.

To answer the question in the title of this article "Is p infinite?": No, but her number of decimal digits is.

My Comments
This calculator aims to enforce human estimation, and cultivate number-sense. More designers / manufacturers / inventors should do likewise by at least trying to make students think.

This question is taken from
the Haese & Harris textbook for IB HL Mathematics and is rather
challenging.Here I present two
solutions.In the first solution, I
eliminate a variable.[ heuristics: H10. Simplify the problem, H11. Solve part
of the problem]And that allowed me to crack the rest of them
problem.In the second solution, I
rephrased the problem in terms of tangents to curves. [
heuristic H09. Restate the problem in another way ] This gives another
angle from which to tackle the problem. Solution 1

We seem to get into a mess here. How can we eliminate k?

Solution 2

Thinking Back

Both solutions are related in
the sense that they hinge on some form of the relation maked as [*]. That
led to an equation in a. Once a is found, k can be found, and the solutions proceed
similarly. The equation [*] is a manifestation of the fact that for a repeated
root, both P(x) and P’(x) share a common factor.