MATHEMATICS INVESTIGATOR SOFTWARE
Fourteen of the 34 investigations on the website have specially designed data-collection software programs
called Mathematics Investigator. Descriptions of these 14 software programs are below and on the following two
pages.
Students may use the Mathematics Investigator software for gathering data and running simulations for the
investigations. Instructors may use the software to demonstrate computer simulations and the process of forming
conjectures and looking for counterexamples. Another purpose of the software is to show students the power and
convenience that comes from using computers and to encourage them to begin thinking of ways to incorporate
computers into the school curriculum.
Titles of Investigations with Mathematics Investigator Software
Triangular Numbers
Consecutive Numbers
Differences of Squares
Integer Differences
Number Chains
Repeating Decimals
Frequency of Primes
Factorizations
Standard Deviations
Dice Roll Simulations
Coin Toss Simulations
Palindromic Sums
Palindromic Differences
Palindromic Decimals
Once one of the 14 investigations is selected by clicking on the Read Me Word file, it is downloaded to the
computer’s desktop. Then clicking on the statement. “Click here to begin the Investigator” will launch the
Mathematics Investigator software. Once this file opens, a description of the specific software will appear with two
or more boxes for entering numbers, as shown in the following figure. This figure illustrates the software for
collecting data for Palindromic Sums. In this example the single number 647 will be tested by clicking OK and the
sums leading to a palindromic number will be obtained. Or, by entering a number from 1 to 50 in the second box,
as many as 50 consecutive numbers (647, 648, . . .) will be tested to determine how many steps are required for
each number to obtain a palindromic number. The downloaded Word file on the desktop for the investigation can be
used in conjunction with the Investigator software by copying and pasting data from the Investigator into the Word
file.
Features such as pull-down menus, editing (cutting, pasting, copying text to other files), and printing are available
for use with the Mathematics Investigator software.
Descriptions of 14 Mathematics Investigator Software Programs
In each of the 14 descriptions, a sample question is posed to illustrate the functioning of the software.
TRIANGULAR NUMBERS: This program will print all the triangular numbers from the nth to the mth triangular
number, such as all triangular numbers from the 76th to the 200th. (Do the units digits in the triangular numbers
form a pattern? See Computer Investigations 1.2)
CONSECUTIVE NUMBERS; Given any whole number, this program determines the ways, if any, that the number
can be written as the sum of two or more nonzero consecutive whole numbers. If you wish to test a range of 50 or
less consecutive numbers, enter a beginning number in the first box and the number of numbers in the second box.
(What types of numbers can be written as the sum of two or more nonzero consecutive whole numbers? See
Computer Investigations 2.1)
DIFFERENCES OF SQUARES: Given any whole number, this program determines the ways, if any, that the
number can be written as the difference of two square numbers. If you wish to test a range of 50 or less consecutive
numbers, enter a beginning number in the first box and the number of numbers in the second box. (What types of
whole numbers can be written as the difference of two square numbers? See Computer Investigations 2.3)
INTEGER DIFFERENCES: For any K integers, with 3 ≤ K ≥ 8, this program places them at the vertices of a
K-sided polygon and computes the difference of pairs of numbers at consecutive vertices, subtracting the smaller
number from the larger. These differences form a new K-sided polygon and the process may be continued as many
times as desired. The computer prints each set of differences and the number of the step. As an example, if four
numbers are selected they are placed at the vertices of a square, as shown below. Then the differences of these
numbers are placed at the vertices of an inner square, etc. (For what values of K will this process produce all zeros
at the vertices? See Computer Investigation 5.1)
NUMBER CHAINS: For any positive integer which is entered and any positive integer entered as a multiplier, this
program will multiply the units digit of the original number by the multiplier and add this product to the number
which is formed by the remaining digits. For example, beginning with a two digit number it will multiply the units
digit by the multiplier and add the product to the tens digit. The resulting sequence of numbers is called a chain,
and the chain is complete when a number in the sequence occurs for the second time. (For any given number and
any multiplier, will the chain always be completed? See Computer Investigation 3.3)
REPEATING DECIMALS: This program prints the decimals for positive rational numbers a/b, with a less than
10000 and b less than 10000. If the decimal is terminating, it counts the number of decimal places. If the decimal
is repeating, it counts the number of digits in the non-repeating part (if any) and the number of digits in the
repetend. (For any prime p, what is the length of the repetend of 1/pn for whole number n ≥ 2? See Computer
Investigations 6.1)
FREQUENCY OF PRIMES: This program lists and counts the prime numbers between two given whole numbers.
(What can be said about the frequency of primes in intervals of 100 consecutive whole numbers? See Computer
Investigation 4.1)
FACTORIZATIONS: This program determines if a number is prime or composite. If the number is composite, all
the factors are printed as well as the number of factors and its prime factorization. If you wish to test an interval of
50 or less consecutive numbers, enter a beginning number in the first box and the number of numbers in the second
box. The computer will print the number of factors and the prime factorization for each number. (What is the
smallest number having 20 factors? See Computer Investigation 4.2)
STANDARD DEVIATIONS: For a given set of data, this program orders the numbers from smallest to largest and
computes the mean, median, mode, and standard deviation. It also prints the percentage of data within ±1, ±2, and
±3 standard deviations of the mean. (Is it possible to create a set of data for which less that 80% of the data are
within two standard deviations of the mean? See Computer Investigation 7.2)
DICE ROLL SIMULATIONS: This program simulates tosses for up to 4 dice and prints the sums until any one or
more of the desired target sums is obtained. For example, for two dice and a target sum of 12 the computer will
print the sums from the tosses until a sum of 12 is obtained. If the simulation is run several times for the same input
(two dice and a sum of 12), the computer will print the mean number of rolls to obtain the sum of 12. ( On the
average how many rolls are needed to obtain a sum of 12? See Computer Investigation 7.3)
COIN TOSS SIMULATIONS: This program simulates up to 100 tosses of a coin and prints a sequence of heads
and tails for each trial. You may select a specific outcome, such as "exactly 3 heads" or "at least 5 heads" or "at
least 4 consecutive heads". After the simulation is run, you may elect to have the trial repeated. After each trial the
ratio of the number of trials with the desired outcome to the total number of trials will be printed. (How many times
do you think a coin would have to be tossed on the average to obtain 3 consecutive heads? See Computer
Investigation 8.1)
PALINDROMIC SUMS: For any nonnegative whole number this program will reverse the digits and add the two
numbers. It will repeat this process of adding the sum to its reverse as many times as desired and print the number
of each step. The operator is informed when a palindromic number is obtained. (Will this process always produce a
palindromic number? See Computer Investigation 1.3)
PALINDROMIC DIFFERENCES: For any two whole numbers this program will reverse the digits and subtract the
two numbers. It will repeat this process, subtracting the difference and its reverse as many times as desired, and
print the number of each step. The operator is informed when a palindromic number is obtained. (For any given
whole number will this process always produce a palindromic number? See Computer Investigation 3.2)
PALINDROMIC DECIMALS: Given any decimal, this program will reverse the digits and add the two numbers.
It will repeat this process of adding the sum to its reverse as many times as desired and print the number of each
step. The operator is informed if a palindromic number is obtained. (Will every two-digit decimal lead to a
palindromic number by this process? Computer Investigation 6.3)