Many years ago, I played Scrabble competitively. One of the first things a beginner tournament player should do is learn the two-letter word list. Recently, I created a worksheet that tests your knowledge of all the valid two-letter words accepted in official tournament play in North America. The worksheet makes extensive use of the StringTools package which has terrific tools for manipulating words.

The worksheet link is below if you'd like to try it out, and I'll...

I recently celebrated my 10-year anniversary at Maplesoft. I've enjoyed my time here, working with a terrific group of colleagues, and I hope to be here for many more years to come. Part of the satisfaction comes from being able to interact with this wonderful user community.

I also celebrated the 20th anniversary of the plot code, parts of which I've had the pleasure of maintaining and improving over the past 10 years. Actually, I believe it is closer to 25 years old...

Just for fun, I'm reviving the Maple soccer ball in anticipation of the FIFA final. You can make a simple animation by adding the option viewpoint=[circleleft] to the display command.

with(plots):
geom3d[TruncatedIcosahedron](p);
V := evalf(geom3d[faces](p));
display(seq(polygonplot3d(V[i], color = `if`(nops(V[i]) = 5, black, white)), i = 1 .. 32), scaling = constrained);

Christopher2222's recent post reminded me of a new plot feature that inadvertently (and through my own fault) got left out of the new-features help pages. The 'filled' option now takes a true/false value or a list of suboptions. The suboptions apply to the polygons that make up the filled region under the curve.

plot(x^2, x=0..1, color="NavyBlue", thickness=3, filled=[color="Blue", transparency=0.7]);

In a recent post, a Maple user misunderstood what an assignment to f(x) meant. Since this is a common source of confusion, I thought it would be worthwhile to say more about this subject.

What is f(x)?
First, f(x) is a "function application" in Maple. It is f applied to the argument x. It is not really the same as what one thinks of as a function in mathematics. Consider a mathematical function such as sin(x+y). In Maple, this can be represented by an expression sin(x+y) or a procedure proc(x, y) sin(x+y) end proc (which can also be written in "operator form" as (x, y)->sin(x+y)). The expression or the procedure can then be assigned to a name such as g. The mathematical function is then represented by g in Maple, and not by g(x, y). Instead, if g is a procedure, then g(x, y) means "the procedure g called with arguments x and y". The "function" help page explains these concepts in more detail.

What is f(x):=x^2 in 1-d math?
Now let's move on to what f(x) := x^2 means. In 1-d math, this means, "Create a remember table entry for procedure f." This stores the expression x^2 so that when you enter f(x), that expression is automatically retrieved, and you avoid the expense of executing the body of the procedure . Similarly, if you enter f(1) := 5, then the value 5 is automatically returned when you enter f(1). Note that if you subsequently enter f(y), you won't get y^2 returned, unless f was already defined to return y^2 with input y. Remember tables are very useful and are heavily used by some Maple library procedures. However, the majority of Maple users do not need to worry about this feature and can do very useful things in Maple without ever knowing about it.