There is no single "most accurate" method of showing the entire surface of the Earth, as all methods involve some degree of distortion. This is because the Earth is a sphere, and it's impossible to flatten a sphere onto a flat surface without stretching or shrinking certain areas.

However, some methods are more accurate than others, depending on what you're trying to represent:

For preserving shapes:

* Conformal projections are good for representing shapes accurately, especially near the poles. Examples include the Mercator projection and the Transverse Mercator projection. These are commonly used for navigation charts.

* Equidistant projections maintain distances from a central point, useful for showing distances from a specific location.

For preserving areas:

* Equal-area projections (also called equivalent projections) accurately represent the proportions of landmasses, but distort shapes. Examples include the Mollweide projection and the Albers equal-area conic projection. These are useful for representing data like population density or resource distribution.

For a balance between shape and area:

* Compromise projections aim to minimize distortions in both shape and area. Examples include the Robinson projection and the Winkel Tripel projection. These are commonly used in atlases and world maps.

Other factors to consider:

* Purpose of the map: What are you trying to show?

* Target audience: Who will be using the map?

* Level of detail: How much information do you need to include?

Ultimately, the "most accurate" method depends on your specific needs. It's important to be aware of the limitations of any projection and choose one that best suits your purpose.

In summary:

* No projection is perfectly accurate.

* Choose a projection based on your specific needs.

* Be aware of the limitations of the chosen projection.