IntMath Newsletter: Finite paint, Perlin Noise, Calcpad

By Murray Bourne, 29 Mar 2018

29 Mar 2018

In this Newsletter:

1. New on IntMath
2. Resources: CalcPad and flim-flam
3. Math in the news: Computer vision
4. Math movies
5. Math puzzle: Book mark
6. Final thought: Bitcoin

1. New on IntMath

(a) The object with finite volume but infinite surface area

Gabriel's Horm

This object has a strange property - we can fill it with paint, but its surface area is so large we can never finish painting it. How is this possible?

The object with finite volume but infinite surface area

(b) Flux - a Perlin Noise example

Continuing the Math Art in Code examples, this one uses an interesting range of mathematical concepts.

Flux - a Perlin noise example

Perlin Noise was an important development in computer game and animations, as it made surfaces a lot more realistic. The process is based on vectors, interpolation and differential calculus. See:

Flux - a Perlin Noise example

2. Resources: CalcPad and flim-flam

(a) CalcPad

CalcPad is a free online programmable calculator that's worth a look. Here's a screen shot:

CalcPad online programmable calculator

It handles a wide range of function graphs, and its output can be saved to Word or printed.

(b) Fibonacci Flim-Flam

Donald E. Simanek, Emeritus Professor of Physics, Lock Haven University of Pennsylvania takes a swipe at the often false claims of those who see the Golden Ratio in just about everything from sunflowers to the art of da Vinci.

Fibonacci Flim-Flam

An enthusiastic critic of pseudoscience takes a closer look at what doesn't conform to the Fibonacci sequence and the Golden Ratio. See:

Fibonacci Flim-Flam.

3. Math in the news: Better computer vision

I'm a big fan of the idea of driverless cars, but there was a tragic accident last week where a pedestrian was killed because the car didn't "see" her. We need better computer vision at night and in fog.

Computer vision in fog

MIT recently announced a successful trial of an improved computer vision system using statistics.

See:

Depth-sensing imaging system can peer through fog.

4. Math Movies:

Here are two recent math-related videos:

(a) Algorithms: weapons of math destruction?

Algorithms - weapons of math destruction

There's a lot of talk at the moment about how Cambridge Analytica used Facebook data to sway the 2016 US election. Are big data algorithms fair and unbiased? Cathy O'Neil doesn't think so.

Watch: The era of blind faith in big data must end

(b) Where do math symbols come from?

Where do math symbols come from?

I have great empathy for the struggles students have regarding math symbols. Here's an overview of why we use them and where some of them come from.

Watch: Where do math symbols come from

5. Math puzzles

The puzzle in the last IntMath Newsletter asked about the sum of the digits of a particular number.

Correct answers with explanation were given by: Twinomugisha, Thomas, Chris, Getnet, Tom Barrett, JDK, Tomas, and Tom Polak. Most of the solutions used the approach of observing what happens with low powers of 10, then extrapolating.

Good on those of you who used the math input system! (Just a note: If you create your math expression in Microsoft Word then copy into the math system you will encounter problems. Best to type it in directly.)

New math puzzle: Lost book mark

Books

In the old days when people read books (^_^), they used a book mark to remember where they were up to. Pedro was reading 4 books and his book mark was left in one of them. What is the expected number of books he needs to open in order to: (a) Find the book mark, and (b) Know which book the book mark is in?

You can leave your responses here.

6. Final thought: Bitcoin power consumption

Bitcoin symbol

The blockchain continues to fascinate people and consume large amounts of media coverage. Electronic currency does have a cost, however - the vast computing resources required to "mine" a new coin require a lot of energy. Alex de Vries started the ball rolling with some eye-watering estimates, and pri.org tries to make sense of it all. Their conclusion:

The most current and widely cited estimates put bitcoin’s yearly energy use at somewhere between 4 and 35 terrawatt-hours. To put that in perspective, all of Google used about 5.7 terrawatt-hours in 2015. [Source: pri.org]

[Hat-tip to Suzanne Bucknell and PiPo for alerting me to some of the items in this Newsletter.]

Until next time, enjoy whatever you learn.

See the 3 Comments below.

3 Comments on “IntMath Newsletter: Finite paint, Perlin Noise, Calcpad”

  1. Chris says:

    B=1/4(1)+3/4(1/3(2)+2/3(1/2(3)+1/2(1/1(4))))=2.5
    2.5 books to find the bookmark
    B=1/4(1)+3/4(1/3(2)+2/3(1/2(3)))=1.5
    1.5 books to know where the bookmark is

    I have no idea what I'm doing ¯\_(ツ)_/¯

  2. stevieX says:

    (a) "Expected" number of books is really the same as "average" number of books. In this case, the probability of finding the bookmark is equally likely for each of the 4 books, so it's

    (1+2+3+4)/4=2.5

    (b) If we haven't found the bookmark after opening 3 books, there's no need to open the 4th, since that's where it must be. So we expect to open the following number of books before we can say for sure which one the book mark is in:

    1/4 xx 1 + 1/4 xx 2 + 1/2 xx 3 = 2.25

  3. Thomas Buckley says:

    It depends on "expect" versus "need"!

    You need to open (a)4 to find the book mark and (b) 3 to know which book it's in to cover the worst case. That's what I expect.

    But I don't expect it to be the worst case always so you could say I expect to open less - so being an optimist 50% - opening (a) 2 to find the book mark will work 50% of the time and opening (b) 2 to find the book?

    1000: Mark in first book - where 1=book with mark 0=book without
    o<-----open book one
    1 book opened to the know the book/1 book opened to find the mark

    0100: Mark in second book
    oo<-----open book one and two
    2 books opened to the know the book/2 books opened to find the mark

    0010: Mark in third book
    ooo<-----open book one, two and three
    3 books opened to the know the book/3 books opened to find the mark

    0001: Mark in forth book
    ooo<-----open book one, two and three
    3 books opened to the know the book
    oooo<-----need to open 4th to find the mark
    4 books opened to find the mark

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