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Books > Fun Mathematics On Your Microcomputer


Fun Mathematics On Your Microcomputer (GB)
Czes Kosniowski
Cambridge University Press, 1983

Download all programs from this book on one disk:


Fun Mathematics.d64

33 programs

Chapter 1: And so on... forever

Program Author Requirements Files Info
Arithmetic Sequences

Pages 7-9.
Czes Kosniowski Unexpanded arithmetic seq.prg
Screenshot
Calculate an arithmetic sequence where the difference between each number is constant. For example, suppose you are given £10 this week with a promise to increase this amount by £2 for every subsequent week. What is the total amount you will have received after fifteen weeks?
Controls:
Follow on-screen prompts.
Geometric Sequences

Pages 10-12.
Czes Kosniowski Unexpanded geometric seq.prg
Screenshot
Calculate a geometric sequence where the ratio between each number is constant. For example, suppose you are given £10 this week with a promise to increase this amount by 10% for every subsequent week. What is the total amount you will have received after fifteen weeks?
Controls:
Follow on-screen prompts.
Harmonic Series

Pages 14-16.
Czes Kosniowski Unexpanded harmonic series.prg
Screenshot
The harmonic series is 1 + 1/2 + 1/3 + 1/4 etc. where the sum gets larger even though the fractions get smaller. This calculates the sum of the harmonic series with a desired number of terms.
Controls:
Follow on-screen prompts.
Calculating SIN(X)

Pages 19-21.
Czes Kosniowski Unexpanded calculating sin.prg
Screenshot
Calculate the sine of an angle in radians.
Controls:
Follow on-screen prompts.
Sequences and Series

Pages 22-23.
Czes Kosniowski Unexpanded sequence series.prg
Screenshot
Single program comprising: Arithmetic Sequences, Geometric Sequences, Harmonic Series and Calculating SIN(X).
Controls:
Follow on-screen prompts.
Intelligence Test

Pages 24-28.
Czes Kosniowski Unexpanded intelligen test.prg
Screenshot
Quiz. Test your intelligence by answering ten problems.
Controls:
Follow on-screen prompts.

Chapter 2: Up and down, round and round

Program Author Requirements Files Info
Graph Plotting

Pages 29-39.
Czes Kosniowski 3K expansion graph plot 3k.prg
Screenshot
Use cartesian coordinates to draw a hi-res plot of five interesting formulas.
Controls:
Follow on-screen prompts.
Polar Graphics

Pages 40-45.
Czes Kosniowski 3K expansion polar graph 3k.prg
Screenshot
Use polar coordinates to draw a hi-res plot of seven interesting formulas.
Controls:
Follow on-screen prompts.

Chapter 3: 5 miles north, 4 miles east

Program Author Requirements Files Info
Treasure Hunt

Pages 53-56.
Czes Kosniowski Unexpanded treasure hunt.prg
Screenshot
Logic game. Treasure is hidden beneath one of the bushes. You move from one bush to another, and pressing * will reveal how close the treasure is. The distance is only printed half the time, and X is displayed if the treasure is more than 10 away. Good players will find the treasure in three moves or less.
Controls:
U (up), D (down), L (left), R (right), * (show distance to treasure).

Chapter 4: Stretching and shrinking

Program Author Requirements Files Info
Matrix Investigation

Pages 61-63.
Czes Kosniowski 3K expansion matrix inves 3k.prg
Screenshot
Use matrices to investigate the effects of rotating or stretching a hi-res picture.
Controls:
Follow on-screen prompts.

Chapter 5: Playing the game

Program Author Requirements Files Info
Two-Person Zero-Sum Game

Pages 66-73.
Czes Kosniowski Unexpanded two-person zero.prg
Screenshot
Use the simplex method to calculate the optimal solution for a two-person zero-sum game.
Controls:
Follow on-screen prompts.
Investment Game

Pages 75-78.
Czes Kosniowski 3K expansion invest game 3k.prg
Screenshot
Strategy game. You have been given $1000 to invest in three companies called X, Y and Z. Each year you must decide how much to invest in each company. You are able to estimate the profit/loss per $1 for thee potential market states, together with the likelihood of each one occurring. Can you make a profit over 10 years?
Controls:
Follow on-screen prompts.
Approximate Game Analysis

Pages 80-85.
Czes Kosniowski Unexpanded approx game anl.prg
Screenshot
Use an approximate strategy to calculate a solution for a two-person zero-sum game.
Controls:
Follow on-screen prompts.

Chapter 6: Rearranging things

Program Author Requirements Files Info
Four Squares

Pages 91-95.
Czes Kosniowski Unexpanded four squares.prg
Screenshot
Puzzle game. Arrange the four squares into clockwise alphabetical order.
Controls:
X (exchange top two squares), T (rotate all squares clockwise), * (end game).
Sixteen Squares

Pages 96-100.
Czes Kosniowski Unexpanded sixteen squares.prg
Screenshot
Puzzle game. Slides the tiles to arrange the squares into alphabetical order.
Controls:
U (up), D (down), L (left), R (right), * (end game).
Twenty-Five Squares

Pages 96-100.
Czes Kosniowski Unexpanded twenty-five sqr.prg
Screenshot
Puzzle game. Rotate groups of letters to arrange them into alphabetical order.
Controls:
1-8 (rotate group), * (end game).

Chapter 7: Wait

Program Author Requirements Files Info
Customer Arrivals 1

Pages 108-109.
Czes Kosniowski Unexpanded cust arrivals1.prg
Screenshot
Simulates arrival times for a situation where customers form a single queue to be served by multiple assistants. This version uses a Monte-Carlo formula requiring approx 60 random numbers.
Controls:
Follow on-screen prompts.
Customer Arrivals 2

Pages 110-111.
Czes Kosniowski Unexpanded cust arrivals2.prg
Screenshot
Simulates arrival times for a situation where customers form a single queue to be served by multiple assistants. This version uses a Monte-Carlo formula requiring approx 600 random numbers.
Controls:
Follow on-screen prompts.
Customer Arrivals 3

Pages 112-115.
Czes Kosniowski Unexpanded cust arrivals3.prg
Screenshot
Simulates arrival times for a situation where customers form a single queue to be served by multiple assistants. This version uses a Poisson formula requiring approx 10 random numbers.
Controls:
Follow on-screen prompts.
Bank Queues

Pages 115-119.
Czes Kosniowski Unexpanded bank queues.prg
Screenshot
Simulates one week in a bank. Enter the number of assistants & maximum queue length each day to see how this influences the number of customers lost.
Controls:
Follow on-screen prompts.
Queue Analysis

Pages 120-122.
Czes Kosniowski Unexpanded queue analysis.prg
Screenshot
Enter the customer arrival rate, customer service rate & number of assistants, to estimate the resulting queue length.
Controls:
Follow on-screen prompts.
Boutiqueues

Pages 123-128.
Czes Kosniowski 3K expansion boutiqueues 3k.prg
Screenshot
Strategy game. You own a boutique that opens for 6 hours per day, 6 days per week. You must decide how many assistants to hire each day, whether to advertise, and whether to offer a 10% discount. Can you make a profit?
Controls:
Follow on-screen prompts.

Chapter 8: Pretty Pictures

Program Author Requirements Files Info
Surfaces

Pages 135-137.
Czes Kosniowski 3K expansion surfaces 3k.prg
Screenshot
Draw a hi-res 3D picture of five surfaces.
Controls:
Follow on-screen prompts.
Contours

Pages 138-144.
Czes Kosniowski Unexpanded contours.prg
Screenshot
Draw contour maps of seven formulas, where the colours show how high/low each part is.
Controls:
Follow on-screen prompts.

Chapter 9: On the move

Program Author Requirements Files Info
Falling Stone

Pages 147-148.
Czes Kosniowski Unexpanded falling stone.prg
Screenshot
Calculate the velocity and distance of a falling stone over a ten second period.
Controls:
None.
Bouncing Ball

Pages 148-152.
Czes Kosniowski Unexpanded bouncing ball.prg
Screenshot
Plot the movements of a bouncing ball.
Controls:
Follow on-screen prompts.
Flight

Pages 153-158.
Czes Kosniowski Unexpanded flight.prg
Screenshot
Simple flight simulator. You must launch a rocket powered aeroplane, reach a height of 500 metres, and land safely.
Controls:
Z (reduce thrust), C (increase thrust), B (reduce angle), M (increase angle).
Flight With Fuel

Page 159.
Czes Kosniowski Unexpanded flight fuel.prg
Screenshot
Simple flight simulator. You must launch a rocket powered aeroplane, reach a height of 500 metres, and land safely. Do not run out of fuel.
Controls:
Z (reduce thrust), C (increase thrust), B (reduce angle), M (increase angle).
Orbit

Pages 159-166.
Czes Kosniowski Unexpanded orbit.prg
Screenshot
Simple flight simulator. You must launch a rocket into orbit around the planet. Do not run out of fuel.
Controls:
Z (reduce up-thrust), C (increase up-thrust), B (reduce side-thrust), M (increase side-thrust).

Chapter 10: Getting bigger all the time

Program Author Requirements Files Info
Exponential Bacteria

Pages 167-169.
Czes Kosniowski Unexpanded expon bacteria.prg
Screenshot
Calculate the number of bacteria in a colony, where they double every two hours (7200 seconds).
Controls:
Follow on-screen prompts.
Growth

Pages 172-173.
Czes Kosniowski Unexpanded growth.prg
Screenshot
Calculate the growth or death of a population using the Euler-Cauchy method.
Controls:
Follow on-screen prompts.
Rabbits and Foxes

Pages 174-178.
Czes Kosniowski Unexpanded rabbits foxes.prg
Screenshot
Simulate the struggle for survival. Rabbits live off the land and foxes eat rabbits. This program calculates what happens to their numbers month by month. On the graphical display, the horizontal position shows 1/20 the number of rabbits, and the vertical position shows 1/2 the number of foxes.
Controls:
Follow on-screen prompts.
Virus

Pages 178-184.
Czes Kosniowski Unexpanded virus.prg
Screenshot
Strategy game. A virus is sweeping the country that turns healthy cells into rogue cells. A new drugs has been produced that destroys both rogue cells and healthy cells. A 600mg dose is fatal, and after an hour 17% of the previous dose still remains in the patients body. Each patient will die if their blood count falls below 1500. You must decide what dose to administer each hour - how many patients can you save?
Controls:
Follow on-screen prompts.
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