• Skip to main content

philcain.com

writing, journalism, books, events, recreation

  • Highlights
  • Work
    • Alcohol Review
    • Alcohol Companion
    • Alcohol for Nerds
  • Not work
    • Stories and distractions
    • Vienna Writers’ Exchange
    • Scene City – Parkour for the mind
    • Netsuke store
  • About
    • Connect

Can you halve yin-yang?

8th March 2023 by philcain


This yin-yang symbol is made of a circle with two semicircles in the middle to define the border between yin (black) and yang (white) areas. Can you draw a single straight line to divide both areas in half?

Reveal the solution
We can start by patiently working out the areas of the different elements of the symbol. We find each quarter of the large circle is πr²/4, where r is the radius of ths circle. We also find that the areas of each of the two semicircles is πr²/8, half the area of the quarter segment of the large circle. That is a crucial “coincidence”. And. moving on, πr²/8 is also the area inside a quarter circle on either side of a line drawn at 45 degrees the horizontal (the red dashed line). If we now pause and tot up the areas of white and black each side of this same line we get 2 x πr²/8 each time. So this line cuts each of the coloured area in half. Job done. Some investigation was needed, but spotting a “coincidence” was really what makes this one click into place almost by itself.

This is a well known one, but it came to my attention again thanks to mindbending maestro Martin Gardiner.

Share this:

  • Click to share on X (Opens in new window) X
  • Click to share on WhatsApp (Opens in new window) WhatsApp
  • Click to share on Facebook (Opens in new window) Facebook
  • Click to share on LinkedIn (Opens in new window) LinkedIn
  • Click to share on Reddit (Opens in new window) Reddit

Filed Under: Story Tagged With: puzzle

Copyright © 2025 · Phil Cain Impressum

Manage Consent
To provide the best experiences, we use technologies like cookies to store and/or access device information. Consenting to these technologies will allow us to process data such as browsing behaviour or unique IDs on this site. Not consenting or withdrawing consent, may adversely affect certain features and functions.
Functional Always active
The technical storage or access is strictly necessary for the legitimate purpose of enabling the use of a specific service explicitly requested by the subscriber or user, or for the sole purpose of carrying out the transmission of a communication over an electronic communications network.
Preferences
The technical storage or access is necessary for the legitimate purpose of storing preferences that are not requested by the subscriber or user.
Statistics
The technical storage or access that is used exclusively for statistical purposes. The technical storage or access that is used exclusively for anonymous statistical purposes. Without a subpoena, voluntary compliance on the part of your Internet Service Provider, or additional records from a third party, information stored or retrieved for this purpose alone cannot usually be used to identify you.
Marketing
The technical storage or access is required to create user profiles to send advertising, or to track the user on a website or across several websites for similar marketing purposes.
Manage options Manage services Manage {vendor_count} vendors Read more about these purposes
View preferences
{title} {title} {title}