Adventures Beyond Reckoning

Where are the maths?

I’m not talking about games like Plushie Tycoon, Petpet Cannonball, or Krawps, which use mathematical concepts like charts, parabolic arcs, and probability. Virtually every activity in Neopia involves mathematical thinking or applications in one way or another. I’m talking about the arcane pleasures of doing maths for their own sake. Prime factorisations. Systems of equations. The zeros of polynomials. Trigonometric identities. But where to find these Diophantine delights?

Fear not, Neopians! Your day of reckoning has arrived. I’m here to guide you through the resources and recreational activities your Neopets have been jonesing for. Heat yourself up some Numbers and Shapes Soup, light some Roodoku Potpourri, and prepare yourself to find that elusive x.

First, make sure you’ve equipped yourself properly. Set up your Bilge Dice Game Table with plenty of pencils and paper, and lay out your Math Blocks and Mathematics Stencil, your Abacus, your choice of calculator (Blue Slorg, Peachpa, or Scorchio), and your Calculation Device. For geometry, you’ll need a protractor (Clear Kougra or Faerie), a ruler (there are a dozen or two available in Neopia, so express yourself!) or, if you can afford it, the incomparable, multipurpose Tyrannian Army Math Tools. Finally, gather some pebbles for your Math Slingshot, so your Neopets can unleash the polynomial power of parabolic projectiles. Now you’re ready to dive into the shelves of mathematical books to be found throughout Neopia!

      Primary Education

     It should come as no surprise that Neopets learn counting from an early age, for one simple reason: potatoes. Perhaps no other single item better represents the heart of Neopia than the humble potato. The youngest Neopets learn colours and numbers in My First Slorg Book, then their letters and numbers in Learning Your ABCs and 123s. Counting lessons continue in Counting Babaas, which serves not only as reinforcement of vital combinatorial techniques, but also teaches important lessons in sleep management and subtle preparation for the more advanced arithmetic they will encounter helping Imiya in Maths Nightmares.

     By far the most important counting activity in Neopia is potato counting, popularised by Alton’s Potato Counter game and Edgar Percival Clarke’s higher-octane sequel, Extreme Potato Counter. Proud indeed is the Neopet who has earned the challenging “Extreme Potato Counter” avatar! Two (count them, two!) separate books are available to help you with this perennial Neopian pastime: Potato Counting for Beginners and the more advanced Counting Potatoes.

     Other books reveal the usefulness of counting. Who can resist the allure of discovering the secret behind Who is Number Two? and just why he is holding up that many fingers? Where is the suspense of The 12th Chime without the inexorable tally? What wonders does the Faerie Activities Book hold, waiting for you to complete the ancient ritual of paint-by-numbers? But these tangents draw us away from our true goal: doing some maths!

     Counting gives way to the more rapid calculations of arithmetic. Here we arrive at the exhilarating joys of addition, subtraction, multiplication, and, most intoxicatingly, division. For many Neopians, this means the most mathematical of all Neopian maths, the eponymous Maths Nightmare. Many resources await you in your quest to help poor Imiya slumber restfully through the night. In addition to the evergreen classic Basic Mathematics, the unassuming Two Tuskaninnies, the hands-on Chalk Board Math Book, and the down-to-earth How to Maths will ground you in the basics. Train yourself to crunch numbers with uncanny efficiency with the Math Textbook, Math Workbook, and the always popular Math Flash Cards. For those seeking to take their mathematical thrills to the highest levels, Maths Nightmare Tips will teach you all you need to know to let Imiya sleep, and perhaps even earn the competitive "Babaa – Maths Nightmare avatar.

     But while Maths Nightmare is the most famous, it is not the only arithmetical pastime to be found. Dice of Destiny devotees will want to delve deeply into the Dice of Destiny Rule Book. Those bold enough to brave the realms of arithmetic that lie beyond multiplication and division will find an invaluable guide in Square Roots-n-More. Finally, those willing to risk the most speculative arithmetic and stare madness in its face can peruse Neovian Genealogy and tackle such mysteries as “Skeith plus Zafara equals... Ixi??”

     Secondary Education

     Mere numbers and simple computations are all well and good, but dear reader, you know that nothing compares to the joys of solving for x. It’s time for your Neopets to put on their big boy/girl/enby trousers and tackle some equations! Start them off with Difficult Equations and the classic standard Algebra. For those Neopets craving some excruciatingly hard sums, move on to the deceptively unassuming Acara Algebra.

     Unfortunately, algebra is relatively unrepresented in Neopia otherwise. Fractions, ratios, and related rates are essential ingredients in the underrated Mathematical Cooking but vanishingly rare elsewhere. No books on graphs and charts are currently published in Neopia, not even pads of graph paper. Polynomials and polynomial functions are, for all intents and purposes, nonexistent in Neopia. Why has King Hagan provided no algebraic counterpart to Maths Nightmare, in which Imiya’s big sister is dreaming of a test where she has to factor polynomials, perhaps with multiple-choice answers? Make an avatar for a suitably high score, Your Majesty, and you would increase the mathematical literacy of a generation overnight and earn the gratitude of maths teachers everywhere.

     Geometry enjoys more breadth of resources than algebra – barely – but less depth. The Large Book of Geometry essentially compiles the material covered in Geometry Level 1, Geometry Level 2, and Geometry Level 3 in a single volume with little additional information. The most important aspect of plane geometry, deductive reasoning, is given painfully short shrift, with not a single book in Neopia dedicated to logic, syllogisms, rigour, proofs, or fallacies. One can only hope that this lacuna will be filled in due course. The only tome coming even close to discussing the nature of proof is the dubious, even outright dodgy, Proof of Jelly Worlds Existence. As extraordinary claims require extraordinary proof, most sensible readers will doubtless conclude that this highly speculative work belongs more in the realm of science fiction than the truth-revealing delights of maths.

     The one exception to the dearth of geometric texts is the surprisingly rich collection of works on architecture, and in particular, pyramids, due to their prominence and cultural significance in the lands of the Lost Desert. Even casual readers will be familiar with the best-selling Lost Desert Architecture; unjustly neglected is Eye-Sha, a truly enlightening biography of one of the great pyramids’ foremost architects. How-to books such as How to Build a Pyramid, its companion volume How to Build a Snowball, the sphere-stacking treatise Bubble Sculptures, and the unfortunately out-of-print Pyramid Painting Vol. 7: Faux Finishes provide practical applications of Euclidean solid geometry.

     Several other books might appear to be windows into the joys of geometry, but do not be fooled! The titles of Square Puzzles, the Square Book of Rainy Day Activities, the Circular Tablet, and The Pyramid Tablets all refer only to the shapes of the book themselves and not their contents. The only exception is the riveting Squares in Nature, one of the only books in Neopia to focus on geometric shapes themselves.

      University Preparation

     Astute readers may have noticed the omission of Kreating Kreludan Angles from the preceding survey of works on geometry. This was for two reasons: we are entering the realm of trigonometry, and Kreludan geometry, due to its gravimetrics, focuses almost exclusively on non-Euclidean geometry. For real-world applications, seek out Mathematics in Space, which deals specifically with mathematics on Kreludor. Assembling Chaos Rays deals entertainingly with the challenges of determining trajectories in a gravity well. For a rigorous look at the underlying pure mathematics, Trigonometry Hyperbolics remains the unchallenged masterpiece. It is one of the most difficult maths books to master, but well worth the time and effort.

     Precalculus texts are uncommon. Readers seeking the joys of vectors, conic sections, or matrices will be disappointed. The best resource for solving problems involving parabolas, How to Make the Perfect Shot, gives an excellent presentation on the relationship between angle, velocity, and force. The few remaining tomes explicating precalculus concepts are Petpetpet Growth Patterns, whose discussion of the logarithms underlying exponential and logistic growth and decay will be the highlight of your Neopets’ summer reading, and Neopian Structural Engineering, an advanced text even by Brightvale’s standards. An honourable mention goes to A Day in the Life of the Bank Manager for its frank, even scandalous, candour about compound interest. We recommend parental supervision for the chapter on amortisation.

     Upon tackling Calculus Basics, your Neopets may be surprised to find the book begins with addition, as it recapitulates key ideas in mathematics from the ground up. You will not find a mathematical monograph with greater breadth than this – we leave it to you to determine if this is a strength or a defect. Alternatively, Korbat Calculus uses Korbats’ flight to motivate key concepts such as extrema, instantaneous velocity, and rectilinear motion. Multivariate calculus, including partial derivatives, differential equations, and advanced integration techniques, appears in the newly-released Theories of Dimensional Time Dilation, making it one of the toughest reads to be found anywhere.

     I can say with a high degree of confidence that more works on statistics are desperately needed in Neopia. Currently, statistics-starved souls must make do with Neopian Statistics and the fan favourite Altador Cup 15 years of Legends and Statistics. (Go, Terror Mountain!) While enthralling reads in their own right, there is less information than you would like on the number-crunching itself, and barely a mention of standard deviations, let alone z-scores.

     Tangents

     This completes our tour of books available on core mathematical topics and their applications. However, there remain a few somewhat tangential areas to consider: computer science, mathematical games, and some interdisciplinary texts that examine the intersection of mathematics with other activities.

     Books on computer science focus on coding. The Programming Book is the industry standard for both novices and experienced professionals alike, while Computer Science for Noobs is a fresh-off-the-press guide for beginners. Programming for Grundos focuses on debugging, an essential skill when dealing with the somewhat sketchy circuitry and software that is Dr. Sloth’s legacy. How to Code for Artists contains indispensable advice on mastering contemporary digital graphics, not to be confused with How to Draw for Programmers, which encourages programmers to tap into their artistic sensibilities.

     Several books on codes exist, which are primarily focused on cryptanalysis, itself a vital branch of applied mathematics which has on more than one occasion changed the course of history. After tackling How to Break Codes and Influence Plot Events and mastering the skills promulgated in Decoding a Coded Decoding Book, your Neopets may finally be ready to take on the challenge on deciphering the mysterious tome known only as The Code.

     Puzzle books abound in Neopia. The best book for arithmophiles is undoubtedly Math Puzzles, the only puzzle book currently available to deal exclusively with maths. Other puzzle books, such as Confusing Conundrums, Neopets Puzzles and Games, Puzzle Magazine, the BIG book of Puzzles, the Little book of puzzles, and Sinsis Puzzle Book, include mathematical puzzles as just one of many other types of puzzles. Geometric puzzle books include the deservedly praised Hissi Mazes, Book of Tangram Puzzles, and Tangram Book.

     Straddling the line between mathematics and art lies origami, which can not only be used to create beautiful art but is capable of solving cubic equations. Neopians are blessed with a surfeit of origami books, including How to make Origami Creatures, Easy Origami Flowers, Origami Pets 101, the Book of Origami Paper, the Korbat Origami Book, the Origami Poogle Pop Up Book, The History of the Origami Warf, and the Origami Pop-Up Book. It is to be hoped that your Neopets will not be disappointed to discover that their focus is more on the art than the mathematics of origami.

     Finally, several books investigate connections with other disciplines. From note duration to time signatures to the circle of fifths and the Pythagorean comma, Musical Math is unexpectedly challenging, especially in the chapters exploring acoustics. Your Neopets will be the envy of their friends with How to Make Math Jewellery, which doubles as a compendium of compass-and-straightedge geometric constructions. Finally, your young scholars will be sure to impress their local Air Faerie with the algebraic approach to magic taught in Advanced Magic.

     I hope that this review of the mathematical literature available in Neopia has been enlightening, and has given you some new ideas and provided some new resources for expanding your Neopets’ mathematical horizons. For those of you, like myself, whose Neopets love maths, there is zero reason to delay. Not to be negative, but it would be odd, irrational, even absurd, to deny your Neopets the very real, complex, transformational, and infinite mathematical delights that await!