Welcome to the Tiny Library


Download The Elements (Ancient Greek: Στοιχεῖον Stoikheîon) is a mathematical treatise consisting of 13 books attributed to the ancient Greek mathematician Euclid in Alexandria, Ptolemaic Egypt c. 300 BC. It is a collection of definitions, postulates, propositions (theorems and constructions), and mathematical proofs of the propositions. The books cover plane and solid Euclidean geometry, elementary number theory, and incommensurable lines. Elements is the oldest extant large-scale deductive treatment of mathematics.
Download Philosophiæ Naturalis Principia Mathematica (Latin for Mathematical Principles of Natural Philosophy), often referred to as simply the Principia, is a work in three books by Isaac Newton, in Latin, first published 5 July 1687. After annotating and correcting his personal copy of the first edition, Newton published two further editions, in 1713 and 1726. The Principia states Newton's laws of motion, forming the foundation of classical mechanics; Newton's law of universal gravitation; and a derivation of Kepler's laws of planetary motion.
Download Fractals, Graphics, and Mathematical Education Excerpts from Chapters 1 and 3, by M.L. Frame & B.B. Mandelbrot. These two chapters discuss the advantages of using fractal geometry as a vehicle for teaching. The ideas of discovery, curiosity, and application. Old, transitional, and "new" math approaches are discussed.
Download The Notes of Ada Lovelace. Augusta Ada Byron King, Countess of Lovelace, made several notes from Sketch of the Analytical Engine invented by Charles Babbage. Of particular importance, found on page 24, is NOTE G: the world's first computer program. What does the program do? In her writing, "enables us to find the value (either numerical or algebraical) of any nth Number of Bernoulli."
Download The Universal Book of Mathematics. By David Darling. A mathematical dictionary, hundred of topics from Abacus to Liouville Number to zeta function.
Link Fractal Garden, created by Rico trebeljahr. A beautifully curated selection of the most famous fractal forms, with animations.
Download Architectural Renderings of Life Drawn with Pencil and Pen by Rafael Araujo, from This is Colossal, 2014. View a small sample of pencil sketches done by hand without the help of a computer. Inspired from sketches of Leonardo Da Vinci.
Download The Mathematical Art of M.C. Escher, From the article, "He was also fascinated with paradox and "impossible" figures, and used an idea of Roger Penrose’s to develop many intriguing works of art. Thus, for the student of mathematics, Escher’s work encompasses two broad areas: the geometry of space, and what we may call the logic of space."
Download The painter who entered the fourth dimension. Did you know Salvador Dalí painted a tesseract? From the article, "Crucifixion (Corpus Hypercubus) unites a classical portrayal of Christ with a shape that only exists in mathematical theory. Dalí’s floating cross is what Banchoff describes as “an unfolded four-dimensional cube."
Download A Statistical Analysis of the Work of Bob Ross. From the article: "Now that we know the basic probabilities of individual tags, we can also find the joint probabilities of some of these events. For instance, how often do a deciduous tree and a coniferous tree appear in the same painting? We know that 57 percent of paintings contain a deciduous tree and 53 percent of paintings contain a coniferous tree. According to our data set, 20 percent of paintings contain at least one of each."
Download Macintosh "Picasso" Artwork....The famous Macintosh “Picasso” trademark logo was developed for the introduction of the original 128k Mac back in 1984. A minimalist line drawing reminiscent of the style of Pablo Picasso, this whimsical graphic implied the whole of a computer in a few simple strokes. It was an icon of what was inside the box, and became as famous as the computer it represented.
Download Explicit formula for finding any Finonacci Number. By Nick Lee. Usually the sequence of numbers is found by recursion, where an = an-1+an-2. This document shows how to find it by using an explicit function.
Download Converting Decimals to Fractions, The algorithm for converting repeating decimals into it's fractional representation.
Download Finding Square Roots, From the 1961 edition of the Encyclopedia Britanica, entry authored by mathematician Howard W. Eves. This is a photograph of a page which explains how to find square roots by hand, using a system similar to long division. Whew! It's work.
Download Finding Roots to Second Degree Polynomial Equations, A two page document showing three methods: by groups, by quadratic equation, and by technology using the TI-84 Plus calculator.
Download Factoring using the "Box Method", A single page document showing how to multiply two binomials. Similar to FOIL, but uses a box structure to keep the student's work organized.
Download Understanding the Fourier Transform, By Steward Riffle. From the article, "an intuitive way to picture the Fourier transform. This may be obvious to you, but it wasn’t to me, so if you work with audio or rendering, I hope there’s something here you find useful."
Download Quora- Calculating Trig Functions, Single page, by Ask A Physicist, this is a brief explanation of how to use a Taylor series to calculate values of Sine and Cosine with a discussion on the accuracy.
Download That Darn River Boat Problem, a detailed explanation of a uniform motion problem (Distance / Rate / Time) that requires a quadratic equation to be solved.
Download The Missing Dollar Problem, A Classic. I borrowed $50 from mum and $50 from dad to buy a bag costing $97. After the purchase, I had $3 left. I returned $1 to dad and $1 to mom, and reserved $1 for myself. I now owe $49+$49=$98 plus the $1 I reserved for myself, which is $99. Where is the missing dollar?
Download Excursion: Mandelbrot Set, This short excursion teaches the hands-on fundamentals of how to generate the Mandelbrot set. Appropriate for students taking advanced algebra or precalculus.
Download Lessor Known Math Terms, Word Document format. Think you know the actual names of things? What is the name of the divider in a fraction? Download to find out!
Download The 15 Commandments of Math. A hilarious yet real windows into the thinking of your math teacher, do not break the commandments!
Download How a Doodler’s Problem Sparked a Controversy in Math, By Jack Murtagh. From Jul 2023. from the article, "Francis Guthrie first conjectured the four-color theorem in 1852 when he noticed that the counties of England only needed four colors to properly fill. He suspected this rule would generalize to any map, but although any kindergartner could understand the question, neither he nor his colleagues could prove it."
Download The Wondrous Connections Between Mathematics and Literature, By Sara Hart. From Apr 2023. from the article, "There have been occasional academic studies on mathematical aspects of specific genres and authors. But the more holistic connections between mathematics and literature have not received the attention they deserve."
Download The perfect age to get married, By Chris Weller. From Feb 2017. from the article, A mathematical theory says the perfect age to get married is 26 —here's why, "So if you're looking for love between the ages of 18 and 40, the optimal age to start seriously considering your future husband or wife is (37% into the 22-year span). Before then, you'll probably miss out on higher-quality partners..."
Download The Math Behind the Hipster Effect, By Alejandro Tauber. From Nov 2014. from the article, "The hipster effect is this non-concerted emergent collective phenomenon of looking alike trying to look different," in the words of Jonathan Touboul, mathematical neuroscientist at the College de France in Paris, and author of the paper."
Download What Moneyball-for-Everything Has Done to American Culture, By Derek Thompson. From Oct 2022. from the article, "The analytics revolution, which began with the movement known as Moneyball, led to a series of offensive and defensive adjustments that were, let’s say, catastrophically successful."
Download Imaginary numbers are real, By Karmela Padavic-Callaghan. From July 2022. from the article, "Sometimes, however, as in the case of imaginary numbers – that is, numbers with negative square values – mathematics manages to stay ahead of experiments for a long time. "ough imaginary numbers have been integral to quantum theory since its very beginnings in the 1920s, scientists have only recently been able to find their physical signatures in experiments and empirically prove their necessity."
Download Kids Guide to Money and Finances, By Matthew Gillman. From December 2021, from the article, Money is an important part of our day-to-day life, but on average, almost half of high-schoolers don’t have an understanding of the importance of good financial literacy and suffer because of it.. This article features a nice selection of online games for elementary, middle, and high school level students. Special thanks to Grayson for suggesting this.
Download A Hitchhiker's Guide to the number 42, The number made famous from the book series by Douglas Adams, this number is the answer to "Life, the Universe, and Everything" but what other interesting properties are there about this number? Read on.
Download The Golden Ratio: Design's Biggest Myth, The golden ratioʼs aesthetic bona fides are an urban legend, a myth, a design unicorn. Many designers donʼt use it, and if they do, they vastly discount its importance. Thereʼs also no science to really back it up. Those who believe the golden ratio is the hidden math behind beauty are falling for a 150-year-old scam.
Download How to Improve your Math, An article from the publication Popular Science. It offers specific startegies on how to become better at doing mathematics.
Download Math genius couple bag $26 Million, Their scheme began in 2003 when Jerry, who graduated college with a degree in mathematics, saw a brochure for a new lottery called Winfall – and realized right away how to beat it.
Download Number Games: Dyscalculia, Brian Butterworth is on a crusade to understand the number deficit called dyscalculia — and to help those who have it.
Download Why it matters if we become innumerate, Companies frequently assume a reasonable level of numerical understanding from their customers. But what happens when the majority of those people in reality arenʼt actually numerate enough to understand the interest rates on their student loans?
Download Math Professor Who’s Fighting Gerrymandering, She realized last year that some of her research about metric geometry could be applied to gerrymandering, the practice of manipulating the shape of electoral districts to benefit a specific party, which is widely seen as a major contributor to government dysfunction.
Download Is Inequality Inevitable?, Although the origins of inequality are hotly debated, an approach developed by physicists and mathematicians, including my group at Tufts University, suggests they have long been hiding in plain sightin a well-known quirk of arithmetic.
Download Why Do Americans Stink at Math?,It wasn’t the first time that Americans had dreamed up a better way to teach math and then failed to implement it. The same pattern played out in the 1960s, when schools gripped by a post-Sputnik inferiority complex unveiled an ambitious “new math,” only to find, a few years later, that nothing actually changed.
Download Maximizing the Expected Value of a Lottery Ticket. By Allen Kim and Steven Skiena, When does it make sense to play the lottery? The abstract reads, "Our analysis demonstrates that this approach increases the expected value each ticket, without increasing the size of the prize pool. We also analyze when ticket sales have maximal expected value, and show that they provide positive returns when the jackpot is between..."
Download The Bernoulli Numbers: A Brief Primer. By Nathaniel Larson. Abstract reads, "In this primer, we explore the diverse properties of a rational sequence known as the Bernoulli numbers. Since the discovery of the numbers in the early eighteenth century, mathematicians have uncovered a vast web of connections between them and core branches of mathematics."
Download One Grain of Rice: Folktale by Demi. For grades 1-8, this Indian folktale is a short story of how one young girl, Rani outwitted the raja, by understanding the power of exponents.
Download The Number of The Beast: 666. Famous as the the "number of the beast" from the Christian Bible Book of Revelations, this integer has been examined and found to be very interesting from a mathematical point of view. Get ready for 10 pages of analysis.
Download Ada Lovelace, What did the first program do?. A brief account of Ada Lovelace, Lord Byron, and Charles Babbage. We learn a little of the backstory on this extrodinary young woman and her insight into how a machine could be programmed, -like a loom- to calculate.
Download Al-Khwarizmi, father of Algebra. Much of al-Khwarizmi’s work with algebra drew heavily on concepts of geometry. In many of his proofs and paradigms, Khwarizmi represents simple numbers and roots as lengths of line segments. The multiplication of roots and numbers represented particular rectangles where the roots and numbers corresponded to the side lengths of the rectangles and their products represented the area of the rectangle.
Download A Brief Taxonomy of Numbers. By Peter James. "I have spent long periods of my life working with numbers. There are many beautiful different types of these that can be constructed (or is that discovered?). The process starts with the first building blocks, the Counting Numbers, which are known more technically as the Natural Numbers. However our journey to discover the nature of numbers will take us into much less familiar territory." Peter's Website
Download Myth: The Bumblebee can't fly? How did this silly myth get started? They can, indeed fly. learn a little bit about of a model of thing doesn't always help us understand how something actually works.
Download Myth Busted: Einstein didn't fail mathematics as a child Sometimes teachers will tell a failing student a short anecdote of how even the great Albert Einstein got poor marks in mathematics as a child. The trouble is, that tale is totally false.
Download Why is "New Math" so Confusing? Chris Everett takes on this criticism of Common Core curriculum with a short and clear explanation. The answer may surprise you.
Download What is the Greatest Mathematical Creation of All time? One person's opinion, √2. Read about why irrational numbers opened a doorway into a yet undiscovered branch of mathematics, and why it caused some hurt feelings.
Download The Witch of Agnesi. Okay, to be fair, not a real witch. Not even a woman burned at the stake. Read about an interesting function curve, the woman who studied it, and how John Colson made a slight mistake in translating her writings from Latin. 🧙🏻‍♀️
RadioLab: Numbers. Aired in 2009. Original Description, "Whether you love 'em or hate 'em, chances are you rely on numbers every day of your life. Where do they come from, and what do they really do for us? This hour: stories of how numbers confuse us, connect us, and even reveal secrets about us." Original Link is here
99% Invisible: The Empire of the Sum. Aired in 2023. Original Description, "But there were also slide rules, metal adding machine, and if you go back far enough, to a time before written numbers even existed: we have the abacus, tally stick, or simply counting things up on our own digits. Regardless of the form it took though, what’s clear is this: without the calculator, our built world as we know it just would not exist." Original Link is here
RadioLab: Zero World. Aired in 2023. Original Description, "Karim Ani dedicated his life to math. He studied it in school, got a degree in math education, even founded Citizen Math to teach it to kids in a whole new way. But, this whole time, his whole life, almost, he had this question nagging at him. The question came in the form of a rule in math, NEVER divide by zero. But, why not?" Original Link is here
Crash Course: Statistics. Fourty four videos, each approximately 12 minutes long, covering a wide range of statistics topics.
View The Map of Mathematics. From DoS - Domain of Science, This video describes "The entire field of mathematics, in a single map!" Honestly, it's very good viewing for students ages 14 and up. YouTube: Link
View e to the pi i for dummies. From Mathologer, Using Homer Simpson, the Mathologer explains how to comprehend how this expression comes to be equal to 1. YouTube: Link
View Visual Proof of the Pythagorean Theorem. From Mathologer, He brilliantly shows how to understand the famous equation a²+b²=c² YouTube: Link
View TED Ed, Where do math symbols come from? Why do we use so many mathematical symbols? Many are discussed, including =, ∑ and ×. (note, see the symbols page for wide selection) YouTube: Link
View TED Talk, What is so Sexy about Math? Cedric Villani, a quirky speaker, Cedric describes how mathematics in the world around us and why mathematics is beautiful. YouTube: Link
View 50 Centuries in 50 Minutes John Dersh. A lecture that details the major developments in mathematics in the last 5000 years. YouTube: Link
View TED Ed, Why Can't You Divide by Zero?An explanation of why dividing by zero can't be done. YouTube: Link
View Teacher Describes Conic Sections. He describes optical illusions (Mirascope) with parabolas, acustic engineering with ellipses, and how GPS triangulation works. YouTube: None
View Creating the Never Ending Bloom. SciFri Arts, John Edmark describes spirals, 3D models, the Golden Angle and how he rotates sculptures to create art. YouTube: Link
Listen Solving for x. TED Radio Hour, Why do we solve for x? Math intimidates a lot of us, but it can deliver surprising answers to life's pressing questions. In this episode, TED speakers discuss the elegant simplicity, and giddy complexity, of solving for X. Source Weblink



Last Updated December, 2023