Incredible Numbers! vs Math Balance

Selected by Apple as Best of 2014, and winner of the 2015 Digital Book Award for Best Nonfiction App. Bestselling author Professor Ian Stewart is your guide through Incredible Numbers. Numbers define the patterns of sunflowers; they bring pleasure through music; and they help us answer existential questions like; ‘How many ways are there to lace my shoes?’ Interactive examples – from simple equations to a working Enigma machine – put the beautiful concepts behind mathematics at your fingertips. “A measure of Ian Stewart’s success is that he’s able to give a clear path through some very hairy mathematics.” – Times Higher Education Supplement There’s so much more than a few screenshots can show: – 23 articles crafted by Prof. Ian Stewart, embedded with 71 groundbreaking interactive demonstrations. – 23 bespoke interactive sections that let you immerse yourself in the beautiful patterns and concepts behind each topic. – 15 of Ian Stewart’s famous mathematical puzzles. Topics include: • Infinity – Explore infinity and understand what it really means to say something is infinite. • Pi – Unwrap the mysteries of pi to see why this strange number is so important and why it’s not just about circles. • Music – Music and math share the beauty of finding patterns in complexity. Detailed interactives show you how they relate in real, meaningful and fun ways. • Codes – See how the power of numbers can unlock complexity in codes. • Nature – See how numbers work in nature by looking at the Fibonacci sequence and how it appears in the real world in beautiful and surprising ways. • Primes – Discover the mysterious patterns in prime numbers, and why they are so important. • Polygons – Get to grips with shapes and polygons. Classical geometry is just another way to think about numbers! • Factorials – How many ways can you lace your shoes? Did you know that if you have 4 eyelets, there are 24 possible lacing styles? With 12 eyelets there are 479,001,600 possibilities. See why this is so in Factorials! Incredible Numbers aspires to convince you that maths is beautiful. Mathematicians know this already. The great solutions and proofs shine to them, but their underlying beauty has been hidden behind abstract algebra and complex equations. Until now. If you enjoy this app, don’t forget to rate it in the App Store.

The Math Balance is a concrete way to explore equations. Begin by placing two weights on the arm so that is balanced, for example the 10-pegs. Then 10 balances 10 which is written as 10 = 10. Using three weights, place a weight on the left 10-peg and use two weights on the right side to balance it, for example 1 and 9. Then 10 balances 1 and 9 and is written as 10 = 1 + 9. The Explore level allows for unlimited exploration of the balance. Up to 10 weights may be placed on each peg. There are four structured categories: Addition, Subtraction, Multiplication, and Division. Each of these topics has a basic level and an advanced level with equations to solve.