A Diagonal Inequality

.
This inequality can be proved by realizing that the square roots in the inequality are the lengths of the diagonals of the four cuboids shown.
Specifically, three cuboids , and of dimensions , and fit inside the cuboid of dimensions corner to corner. Call the corners , , and . The diagonal of cuboid is , and the length of the broken line is the sum of the diagonals of , and , which is , due to the extended triangle inequality.

SNAPSHOTS

  • [Snapshot]
  • [Snapshot]
  • [Snapshot]

DETAILS

Reference
[1] N. Stojanović, "Proof without Words: Inequality for the Sum of the Diagonals," The Mathematical Intelligencer, 43(4), 2021 p. 32. doi:10.1007/s00283-021-10075-9.
    • Share:

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.