The Textbook of the Future

# Discovering Mathematics

When teaching mathematics at school or university, it is almost always presented as a linear, complete and coherent curriculum. We start with simple things like integer arithmetic or axioms, and then move on to more advanced topics that build upon what we already know.

But this is not how mathematics was developed throughout history: it took centuries before new ideas became widely accepted. New discoveries were often random, accidental and non-linear. Most of the work done by mathematicians throughout history was incorrect, lead to dead ends, and was soon forgotten — only the few correct results or interesting theorems were…

# Mathigon Teacher and Parent Accounts

If you are using Mathigon as a teacher in classrooms, we have some big news. In our latest update, we’ve added one of the most requested new features: teacher and parent accounts!

When you create a new account at mathigon.org/signup, you can now choose between three different account types:

If you already have a Mathigon account, you can go to mathigon.org/settings and convert your existing account (as long as you are at least 16 years old):

# How to build an equation editor

Mathigon’s next course will be on quadratic equations, and an important part is a new equation editor and parser. This turned out to be one of the most complex components we’ve built — here are some of the requirements:

• We need to be able to display complex equations, including nested fractions and square roots.
• Students need to be able to type equations, including on mobile devices.
• We need to be able to parse students’ equations to check if their answer is correct or to diagnose what mistakes they made.
• We need to be able to animate between two consecutive equations…

# One Million Digits of Pi

Earlier this month was Pi day, and we published a brand new course on Circles and Pi. Part of this course was a list of the first one million digits of pi, which you can scroll through and even search for specific patterns (like your date of birth):

It is widely believed that Pi is a normal number, which means that any string of digits should appear somewhere in its decimal expansion. However, mathematicians have not actually been able to prove this yet!

Building the component was not easy: usually showing this much text on a website will crash your…

# Trisecting the angle — it’s possible!

In ancient mathematics, one famous kind of puzzle was constructing certain geometric shapes using nothing but a straight edge and a compass.

These tools might seem very primitive, but they were easy to build with sufficient accuracy. They also avoided dealing with units, of which there wasn’t a standardised system like we have today.

The construction of some geometric shapes, like an equilateral triangle, is very simple:

Other constructions, like the regular 17-gon, are much more complicated and were not discovered until thousands of years later, by genius Carl Friedrich Gauss:

# Times are Changing

## Clocks are becoming more human

Today the International Geographical Union and the American Society of Cartographers have announced the introduction of a single new time system to replace the existing 24 timezones. The Continuous Standard Time (CST) changes continuously around the globe and will have a profound impact on our lives.

# Lunchtime is an Illusion

Most readers will be familiar with the disconcerting feeling after long haul flights: jet lag, or desynchronosis. This effect is not caused by the time difference between origin and destination, but because you cross multiple time zone boundaries.

The human body, our “biological clock”, is fundamentally continuous and extremely sensitive to…

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