My research programs can be found here.

Calculators are organized by topic. See the bottom of the page for notes on how to install the TI-86 and TI-83 programs.

Contents


Pascal's Simplices (project)
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    		• Pascal's simplices Mathematica notebook: Contains functions that compute and display cross sections of multidimensional Pascal simplices. The first ten rows of Pascal's tetrahedron and the first ten rows of Pascal's pentatope are computed as examples.

    Pythagorean Triples (project)
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    		• List of Primitive Pythagorean Triples
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    		• Pythagorean triple finder: Finds all primitive Pythagorean triples with hypotenuses within a given range.
    TI-86 (needs zstate): Finds primitive triples with increasing hypotenuses, starting at a given integer, until EXIT is pressed. Displays current side lengths for progress determination.    		Working
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    		• Pythagorean triple generator: Gives the Pythagorean triple generated by two numbers.
    TI-86 (needs zstate).    		Done
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    		• Pythagorean Triples Modulo p: Gives all solutions to the Pythagorean equation modulo a given prime p.

    Regular Polygons (project)
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    		• Regular polygons Mathematica notebook: Contains functions that compute the following geometric quantities of a regular n-gon of radius r: side length, interior angle, sum of angles, area, perimeter, apothem, and median length. Contains functions that compute the following combinatorial quantities of a regular n-gon with its diagonals drawn in: number of diagonals, number of intersection points, number of (total) regions, and number of edges.
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    		• Regular n-gon Calculator: Computes the number of intersections, segments, and regions formed by the diagonals of a regular n-gon as well as the number of diagonals, side length, angle measure, area, perimeter, and the length of the diagonals.
    TI-86 (needs zstate and zvar), TI-83 (needs ZP and ZR): Draws the polygon. Includes the ability to zoom in on the upper right quadrant of the drawing. Computes the lengths of up to fourteen diagonals. By default, circumscribed circle has diameter 1; this can be changed by setting "Number of sides" equal to 0.    		Paused

    Regular Polyhedra (project)
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    		• Regular polyhedra Mathematica notebook: Produces images of the five Platonic solids. Contains functions that compute the following geometric quantities of regular polyhedra of side length s: volume, surface area, radius of circumscribed sphere, and radius of inscribed sphere (apothem). Also contains functions that compute the number of vertices, number of edges, and number of faces of each of the Platonic solids.

    Miscellaneous Calculators
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    		• JavaScript PlayGround: A JavaScript compilation calculator extended by thirty mathematical functions.
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    		• Chinese Remainder Theorem: Solves a finite system of linear congruences x ≡ ai mod mi, where the moduli mi are pairwise relatively prime.
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    		• Age Calculator: Computes the number of days between any two dates C.E. in the Gregorian calendar. (Y2K-exempt!)
    TI-86 (needs zstate), TI-83 (needs ZP and ZA).    		Done
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    		• Change of Base: Converts a value in an integer base to another integer base, representing a value as a list of place values when necessary.
    TI-86 (needs zstate).    		Done
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    		• Factor: Factors an integer into its prime factors.
    TI-86 (needs zstate), TI-83 (needs ZP): Displays, in increasing order, the prime factors of an integer less than 1014. The list of factors is stored as the variable LIST.    		Paused
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    		• Fibonacci Sequence Calculator: Computes any term (less than the 1475th) of the Fibonacci sequence and can subsequently compute previous and next terms.
    TI-86 (needs zstate), TI-83 (needs ZP): Can compute up to the 4784th term.    		Paused

    TI-86 and TI-83 Programs

    You may download all TI-86 programs or all TI-83 programs on this page (zipped).
    TI-86 Programs: All programs for the TI-86 require the subroutine zstate. Additionally, the programs Regular n-gon Calculator and Polynomial Manipulator require the subroutine zvar. zstate preserves your window settings, Radian/Degree setting, and yN= equations. However, if you have important data in any variables (especially A, B, C,...) (or the stat plot lists when using American Flag), assure that the program you are using does not interfere with this data; otherwise it may be overwritten. zvar clears the variables A, B, C,... for use by the programs that call it.
    TI-83 Programs: All programs for the TI-83 require the subroutine ZP. Additionally, Regular n-gon Calculator requires the subroutine ZR, and Age Calculator requires the subroutine ZA. ZP preserves certain settings, ZR clears the variables A, B, C,... for use by the program that calls it, and ZA contains information regarding the number of days in each month.

  		• American Flag: Draws an American flag and includes the option to store the picture.
    TI-86 (needs zstate).    		Paused
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    		• Eye: Draws an eye and includes the option to store the picture.
    TI-86 (needs zstate), TI-83 (needs ZP).    		Paused
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    		• n-Degree Regression Calculator: Computes the coefficients of the n-degree interpolating polynomial to the first n + 1 data points in xStat and yStat, and graphs the function (as y1) and the data points. Stores the list of coefficients as B.
    Note: Rather than using the point (0, 0) as a data point, use a close approximation such as (10–6, 10–6); for some reason PNReg has difficulty when n > 9, which results in a matrix whose determinant is 0, which the Simult operation cannot handle.
    TI-86 (needs zstate).    		Paused
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    		• Newton's Method: Displays a table of iterations of Newton's method of approximating a root of a differentiable function.
    TI-86 (needs zstate).    		Paused
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    		• Polynomial Manipulator: Adds, subtracts, multiplies, divides, raises to natural number exponents, differentiates, and integrates polynomials of one variable by representing them as lists of coefficients organized from greatest- to least-degree term. Stores most recently outputted list to LIST.
    TI-86 (needs zstate and zvar).    		Paused
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    		• p-series Summation Calculator: Computes ζ(p) / πp, the rational factor of the Riemann Zeta Function ζ(p) for positive even p. Stores the result as C.
    TI-86 (needs zstate).    		Done
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    		• Summation of Consecutive Powers: Expediently computes for given positive n and p.
    TI-86 (needs zstate).    		Done