So it seems that not everybody is on board with the idea of Apple launching a 10.5-inch iPad sometime this year, with even such a noted Apple expert as Daring Fireball’s John Gruber saying on The Talk Show “It doesn’t make any sense to me.”
However, co-founder of Studio Neat, Dan Provost, has written a great blog post that explains in mathematical terms exactly why it makes perfect sense for Apple to release a 10.5-inch iPad, and he’s even convinced Gruber, who shared Provost’s theory on Daring Fireball and said, “Can’t believe I didn’t think to do this again regarding this rumor. The math works out.”
And indeed it does. Provost’s theory is based on Phil Schiller’s original announcement of the 12.9-inch iPad Pro, back in September 2015, when he said that Apple had decided on that particular size for the iPad Pro because the width of the new iPad was exactly the same dimension as the height of the 9.7-inch iPad, meaning that it could still display two full-height iPad apps side by side.
And with the rumoured new 10.5-inch iPad it looks like Apple is repeating the trick, but this time with the iPad mini. Here’s a direct quote from Provost:
“The math works out perfectly. This new 10.5-inch iPad would have the exact same resolution as the 12.9” iPad Pro (2732x2048), but the same pixel density of the iPad mini (326 ppi instead of 264 ppi). Crunch the numbers, do a little Pythagorean Theorem, and you end up with a screen 10.5” diagonal (10.47” to be precise, but none of Apple’s stated screen sizes are exact). In terms of physical dimensions, the width of this 10.5” screen would be exactly the same as the height of the iPad mini screen.”
So, essentially, the new 10.5-inch iPad would have “the resolution of the 12.9” iPad Pro, but the form factor of the 9.7” iPad Pro.”
Source: https://blog.studioneat.com/why-would-apple-release-a-10-5-ipad-ca4441f7f628#.9oavhn9ra