A surprise parabola and more garden

Idly wondering about the tangents from a point to a circle I constructed the figure below. The point A is on a circle and can be moved round the circle. The chord CD then moves around. The interesting thing is to see the envelope of this chord as the point A is moved. ..

parabola surprise constructio

Circles and hyperbolas galore, but when the big circle passes through the centre of the smaller circle the envelope is the surprise parabola. The question is “How do I find the equation of such a parabola? Sensible choice of origin and axes is the first thing. the y-axis is best as the line joining the centres of the two circles. Then you need an equation for the line CD, with a suitable parameter. Then a little bit of calculus………..Nice one for calculus students

parabola surpriseConstructions done with my web based program. Try it yourself: GEOSTRUCT

And now for January in Puerto Rico. I don’t know the name of the pink and white flowering tree, but I do know that without my machete the whole garden would be infested with babies from the first one.


This one below is a yellow eleconia, also spreading madly.


And this is a cute little tree with probably poisonous berries.


And what the hell have they done to the post editor. It only works in BOLD

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Too Close for Comfort, a “must read” link

Forecasting the future of “education”, by Eli Horowitz

Prescient ??????

View story at Medium.com

View story at Medium.com

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Filed under education, future, horrors, humor, satire, school, transformations, Uncategorized

Mathematics in my garden

So there it was, built from one clothesline to another, glistening in the sunlight one morning last week:


A near perfect spiderweb, demanding a better photo:

Here is  the horizontal strip, showing the variation in spacing of the spiral:

and again, with a superimposed scale. The spider is at the centre.spiderweb cropped with dots

And now rotated, to give more detail.spiderweb cropped with dots rotated

Now “Get modelling!”.


Filed under algebra, geometrical, Puerto Rico, series, teaching, tropical garden, Uncategorized

CBE and computer programming

What hope can there be for Competency Based Education, by computer of course, if commercial programmers continue to come up with this sort of stuff?

computer program oops



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CBE is not for me, in verse

“Mathematics, take a break, the doggerel has come back !”

Today I start to fill my pail.
Through the next test I will sail.
Common sense must then prevail:
I’ll clear my brain of what’s now stale
To make some space inside the pail.
For competence, the holy grail,
Ensures that I will never fail,
Though moving forward like a snail.
* * * * * * * * * * * * * * * * * * * * *
The whole damn thing’s to no avail.


Filed under education, testing, tests, Uncategorized, verse

What exactly is Base 10 arithmetic ?

Teacher: “Now we’re going to learn about base 10 arithmetic”.
Wise guy: “Is that where 3 + 4 = 12, or is it where 3 x 4 = 12 ?”.

I did a search on the net and found the term “base 10” all over the place. What does it mean?

An apparently annoying question:
“Does the 1 in 10 stand for the number 10’s in 10?”.

The interpretation of 10 in the system described as “Base 10” depends on the base of the system, so what is it? How do I find out?

We have here a logical problem. The term “Base 10” as a definition is self referential. It is more subtle than this definition of a straight line:

“A straight line is a line which is straight”.

The problem arises from the almost universal confusion between the two things:
1: The name of a number, in this case “ten” is supposedly implied
2: The symbols representing a number, in this case 10 in the base ten system”

So the answers to the questions “What is it? How do I find out?” above are “Unknown” and “You can’t”

Writing “Base 10” when you mean “Base ten” is probably the first step in making math meaningless.



Filed under abstract, arithmetic, confusion, definitions, language in math, math, teaching

divide by zero: why not?

Optional thought: Just read it.

Resource Room Dot Net Blog

Student couldn’t *quite* remember how she had remembered why you can’t divide by zero, and she started by saying “I knew 0 / 9  was zero because …”   and she drew a 9 and the “gazinta” and the 0, and yes, you could put a “zero” on top and do standard long division.

So, taking that cue, I put the zero on the out side and asked, “what would you put on top so that 0 x that was 9? ”  And since nothing made sense…

A nice visual…

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A. N. Whitehead on negative numbers (1911)

This is really worth reading. It is from his book, “Introduction to Mathematics”, published in 1911.

whitehead intro to math negative nos





Filed under abstract, arithmetic, Number systems, teaching, Uncategorized

One arrested in Knoxville math lab raid

There’s many a true word written in jest !

Mean Green Math

A friend from Tennessee sent me this jewel recently.

Math Lab raid

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EngageNY Math, now Eureka, A Common Core Dropping

When I first looked at Engageny math I thought “ghastly”.
I am not alone. Read on…..

IGNITE! ... Fire is Catching

There is an elephant in the room…

And this elephant is creating quite the stench.

The numerous discussions happening around the country regarding EngageNY, a “free” math program, are snow balling. More and more school districts are considering adopting this program, as others are dumping it (no pun intended).

What do you know about it? Where did it start? What’s its history? Is it “free”? How much did it cost to write? Who wrote it?

Or a bolder question: What in the H. E. double hockey sticks is this?

ComplicityI’m often tagged and asked to join discussion threads with these questions, amongst numerous others. I’ve been very vocal about my thoughts regarding this math program, and my angst regarding what harm it is causing children.  I do not fear discussing the elephant in the room…  especially an elephant causing such a stink. How could I not speak up? As a 26 year math educator, I…

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