Apart from using a knife (or not) and cutting up an apple I can think of predominantly two ways of eating an apple. This does matter because one way is correct and the other is not so correct.
Circumferential or the Segment method?
A circumferential eater will take a bite, rotate the sphere using the core as the axis and take another bite. This will result in a curve of apple exposed around the great circle of the apple. Then another line of bite is taken from each end (assuming that the eater has a big enough mouth to bite to the core)
A segmental eater takes bites out of the apple from stalk to opposite pole. This results in a segment being eaten and then the apple being rotated to start the process again.
The problem is exposure of the flesh of the apple to the air to turn brown and this needs to be minimised. In the segment method the area exposed for significant time is constant. For the circumferential method the area exposed increases with time.
Which leads to:
The analysis shows that if your bite radius is greater than 0.140 of the radius of the apple then you should eat in segments. Apart from small mammals the bite radius is going to be more than 14% of the apple radius, unless there is a huge apple variety waiting to be discovered.
This post was necessary because every time I eat an apple my wife tells me I am eating it the wrong way.