S ± <n> or
P ± <n>

Shows curves offset from squares or pronics..

Use these commands to display product curves as shown on the website. For example, if you type:

s   –   4

you'll see the curve which is parallel to the squares with 5, 12, 21, etc.

You can display the same curve with the coe command by typing:

coe   1   0   –4

The coe command is more powerful but a little more complicated to use.

mod <a> <b>

Shows congruence class.

This command highlights all numbers in the spiral that are congruent to a modulo b.

For example, if you enter

mod  2  5

The program will draw a green circle around every number n such that

coe <a> <b> <c>

Analyzes sequence and, optionally, draws associated curve.

Enter the three coefficients of a quadratic formula. (All the offset curves on the website are quadratic). Press "do it" to analyze the generated sequence in the command window. Press "graph it" to draw the formula's curve in the graph window.

For example, if you type:

coe   4   –8   41

you will see the curve for the quadratic formula:

4x²  –  8x  +  41

seq <n1> <n2> <n3>

Analyzes sequence and, optionally, draws associated curve.

This does the same thing as coe, except you enter any three successive numbers from the sequence instead of the formula's coefficients. (You can also do the same thing in a third way, by double-clicking three numbers on the graph and pressing G.)

For example, if you type:

seq  16  25   36

you will see the curve for the perfect squares.

ang <fraction | denominator>

Shows angle lines to help visualize offset curves.

You can type either a fraction or a whole number as the argument. A fraction designates an angle in rotations. For example, if you enter

ang 1/4

a line will be drawn 1/4 of the way around the spiral on the 90-degree line.

If you enter a whole number, a line is drawn for every fraction that has that number as a denominator. For example, if you type

ang 5

the program draws lines at 0/5, 1/5, 2/5, 3/5 and 4/5 rotations.

off <fraction [quantity]>

Shows offset curves for any given angle.

This command draws offset curves for the specified angle. (In this program, an angle is described as a fraction of a rotation. For example, 180 degrees is 1/2.) For example, this command:

off 3/7 100

draws the first 100 offset curves that are parallel to (and counterclockwise from) angle 3/7.

If you omit the quantity, the program displays the first 30 offset curves by default. For example, this command:

off 19/34

draws the first 30 offset curves that are parallel to angle 19/34.

Be careful with large denominators and large quantities; your computer may bog down and take a long time to draw the screen.

Offset curves are shown in three colors: gray indicates curves that contain primes; red indicates curves that are purely composite (except for the first and possibly second memberr) due to the fact that the sequence is "even"; and blue shows curves that are purely composite (except for the first and possibly second members) because the fractional part of their distance from the angle contains a perfect square in the numerator.

Fac stands for factors. This command draws two offset curves (one product curve, one factor curve) for the specified numbers.

For example, if you want to see the curves for the multiplication 71 x 1832, you would type:

fac  71  1832

and a pair of curves will be drawn on the graph.