VJOURNAL SMART BOOK · Volume I · How numbers and shapes work
Mathematics
Eight chapters, each with a living drawing and a sandbox: numbers, fractions, Pythagoras, pi, algebra, graphs, growth and chance.
Start readingMost maths books give you a rule and a page of exercises. This one lets you see why the rule is true. Beside every paragraph a drawing plays the exact moment the text describes: an odometer rolling from 999 to 1000, four triangles filling a square, a wheel unrolling a length of pi, balls piling up into a bell curve.
Each chapter has five moments. Read a block, press play, and the drawing jumps to its moment; scrub back and the moment returns exactly as it was. Under the picture there is a sandbox with sliders, so you can change the numbers and compare the result with the worked example in the text.
Contents
- 01Numbers and place valueFrom tally marks to zero and binaryLong ago people counted with scratches on bones. Today we write any number with just ten digits, because the place where a digit stands tells you how much it is worth. Zero holds the empty places.
- 02Fractions, ratio and percentParts of a whole, from Egypt to the shopA fraction tells you how many equal pieces of a whole you have. Cut a bar into four equal pieces and one piece is a quarter. Percent is just a fraction whose whole is one hundred.
- 03Pythagoras and right trianglesFrom Babylon to your phoneIn a triangle with a square corner, the square on the longest side is exactly as big as the two other squares together. For sides 3 and 4, the long side is 5, since 9 + 16 = 25.
- 04Pi and the circleCircles, Archimedes and endless digitsTake any circle and measure around it, then across it. Around is always a little more than three times across. That number is called pi, and it is about 3.14.
- 05Algebra: equations as a balanceFrom balance scales to al-KhwarizmiAn equation is a balance scale. If you do the same thing to both sides, it stays level. That lets you find the hidden number x one small step at a time.
- 06Functions and graphsFrom Descartes to wavesA function is a rule: put a number in, get a number out. Draw every pair as a point and the rule becomes a picture, such as a straight line, a U-shaped curve or a wave.
- 07Growth, doubling and halvingFrom chessboard grains to carbon datingAdding the same amount each day makes a straight line. Doubling each day makes a curve that shoots up. Halving does the opposite, and the number e belongs to growth that never pauses.
- 08Probability and chanceFrom coin tosses to the bell curveProbability is a number from 0 to 1 that tells you how likely something is. A coin lands heads half the time, and many random bounces pile up into a bell-shaped heap.
VITON13 LAB
Keep studying on the LAB table
Open the chapter's experiment, timeline or map on VITON13 LAB, with your notes as a document beside it.
Open VITON13 LABAbout this book
How does the animated maths textbook work?
Every chapter pairs a text with a living drawing. The text is split into blocks, and each block belongs to one moment of the drawing. Scroll to a block or press its play button and the picture shows that moment. You can pause, scrub the timeline, and use the sandbox under the picture to try your own numbers.
Do I need to be good at maths to follow it?
No. Every idea is first told in plain words, then written as a rule with each symbol explained, and then used once on real numbers. If a formula looks scary, read the plain-words sentence before it. You only need arithmetic to start, and each chapter builds on the one before.
What does the maths textbook cover?
Volume I has eight chapters: numbers and place value, fractions and percent, the Pythagorean theorem, the number pi, algebra, functions and graphs, exponential growth and halving, and probability. Each chapter has a short version for younger readers and a list of sources.
Are the historical stories in it all proven?
No, and the text says so. Dates and discoveries such as Brahmagupta's rules for zero in AD 628 or the 1654 letters of Pascal and Fermat are well documented. Stories such as the Egyptian rope-stretchers or the chessboard grains are marked as legends or uncertain, so you can tell what is evidence and what is a tale.