Calculating the twin paradox using length contraction

A common question about the twin paradox is, where is the asymmetry? And the common answer is, only one of the twins accelerates. I think there's a simpler explanation: The traveling twin ages less because that twin's path is shorter, due to length contraction. Traveling a shorter distance at the same velocity (at any given instant) takes less time.

Below is math to support that assertion, in units where the speed of light = c = 1 (e.g. 1 light year / year). The variables are defined at the relativistic rocket site. Let Bob be the Earthbound twin, and let Sue be the traveling twin. Note that both Bob and Sue make a trip relative to the other.

[; T = \sum \Delta T = \sum \frac{\Delta d}{v \gamma} = \sum \frac{\Delta d \sqrt{1 - v^{2}}}{v} ;]

This shows that Sue's aging can be calculated by summing the time elapsed on her clock to traverse each length-contracted (as she measures) segment of her trip, where each segment is small enough that the velocity in that segment can be deemed to be constant. In other words the twin paradox can be explained using only velocity, no acceleration required, which agrees with the clock postulate:

[The gamma factor for time dilation] depends only on v, and does not depend on any derivatives of v, such as acceleration.

here is code, written the Go language, to verify the math. Choose the Run button. Search the relativistic rocket site for "Here are some of the times you will age when journeying to a few well known space marks, arriving at low speed". The code calculates Bob's and Sue's aging (time elapsed on their respective clocks) as Sue makes a trip from Earth to the midpoint between Earth and Vega, accelerating at 1 Earth gravity the whole way. To include Sue's deceleration from the midpoint to Vega, double the values that are output.

The code outputs:

While Bob aged 14.44 years as predicted by the relativistic rocket equations, Sue aged:
  3.29 years as predicted by the relativistic rocket equations
  3.29 years as predicted by the numerical integration herein

Here is another relationship that shows the twin paradox can be explained using only velocity, no acceleration required:

[; T = \sum \frac{ \Delta d \sqrt{1 - v^{2}}}{v} = \sum \frac{v \left (\Delta t\right )\sqrt{1 - v^{2}}}{v} = \sum \Delta t \sqrt{1 - v^{2}} ;]

This shows that Sue's aging can be calculated by summing: the time elapsed on Bob's clock to traverse each segment of his trip, divided by gamma.

What do you think? I can show separately that gravitational time dilation can also be explained by length contraction.