Regional Border Planning
Any unplanned borders made by "nature, history or social mobility" have to be considered when designing or re-designing a province. A geometrically designed province border is more legitimate and economical, but can be partially temporarily impractical, until the state has more control over natural, social and political factors.
Natural borders are those made by mountains, waters, forests, desert, etc. Social borders are made by the concentration of similar groups of people. Historical borders are based on old agreements between countries or provinces within a country.
Nature's borders are more important and stable in deciding a province's shape, than those made by the movement and settlement of humans. However, the more humans control and refine "nature" and "themselves," the more geometrical shapes are needed, as the latter are most efficient in achieving equality, which is based on rules and planning, not arbitrariness and randomness. LOGIC is more stable than NATURE, which is in turn more stable than PEOPLE.
No one should change regional borders, between a country's regions, except its central government. As for international borders, between countries, they can only be changed by agreement between states, or an unbiased arbitrational powerful world body if there is any: a world government or a "restructured" UN. EQUALITY is the objective of any border design, of a country, an alliance of countries, or a whole world order, achieved by just laws and rulers.
When colonial powers were dividing colonies among themselves, as in Sykes-Pico Agreement, according to their mood and interest "then," they neither considered nature nor logic, which later led to serious troubles and conflicts within and among such colonies when they gained their independence. (And the usual answer from colonial powers is that colonies aren't mature enough to solve their conflicts!) In the same manner, the US and its neo-colonial allies sought a New World Order at the 21 century that only serves those rich countries' interest and ignores the rest.
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Provinces are best shaped into equal circles within HEXAGONS bordering other hexagonal provinces, for minimum distance between ends and centers, and also safer, more cooperation with other provinces. The equal distance from center to all ends of the province allows maximum control, supervision and security, and minimum cost of transportation, communication, and other infrastructures. Usually, any other province shape is less advantageous.
A circular shape would've been perfect hadn't it been for the empty no-man's space between circles. However, a hexagonal shape can still include a circle within, for optimum governance, where the small space between the circle & hexagon it lies within can be ideal for inter-province traffic. One can still stay close to the ideal all-reaching circle shape, by creating smooth circular inter-provincial intersections between hexagonal provinces.
Even a circular island, or one with any other shape, is best included within hexagonal borders formed by its territorial waters.
Yet, a square is better than a hexagon sometimes. Although a hexagonal "beehive" shape has the closest distance between center and ends (compared to a square shape), and more shared borders that allow more inter-provincial movement and cooperation, YET, it's problematic, esp. regarding remote border-provinces adjacent to "other countries," with one hexagon up, another down, causing difficulty controlling and defining its six obtuse angles, compared to the simple right-angled straight-bordered four-sided adjacent shapes like squares or rectangles.
A rectangular "strip" shape is problematic too for many reasons:
A more random, less defined shape wastes time recognizing its needs & connecting with its subdivisions, and causes disputes with neighbors as well.
Any partly/fully land-locked region inevitably loses some of its autonomy to the surrounding region(s).
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There are large provinces with inevitably large uninhabitable, restricted or protected spaces. Uninhabitable areas need more research and exploration till they are inhabitable and properly benefited from. It's better to divide the large unused space, among many provinces, than allot it to one lucky/unlucky province, to encourage people from all over the country to explore, improve and inhabit it.
Some provinces have higher population than others, for economic, social, historical ... reasons, which ALWAYS creates inequality. The state should plan and facilitate the re-distribution of population, for a fair balance between population and resources.
In the US, California and Texas should be divided into more states, in terms of size and population, until they reach the "average" every US state should have. If the population of the "new" states still exceed such US average, some Californians and Texans should move to the rest of the country, mostly to Mid-West states that are large in size and small in population. Meanwhile, New England states should merge into fewer ones, and most of their population should also move elsewhere in the country.
As for life quality, both regions of West Coast and New England have powerful media, scientific institutes, health service, etc. than most other regions, which is better than not having any nationwide (otherwise citizens travel abroad for treatment, studying, etc.). Although specialization is good for diversity and cooperation, every state still deserves to be advanced in the basic fields of living (health, housing, research, media outreach ...). State diversity is good in careers, natural resources, tourism, etc. but not in basic living necessities.
However, since full equality and self-sufficiency are almost impossible; they can be achieved relatively. For instance, there can be diversity within the type of services each state can focus on, according to its natural resources and urgent needs, especially in coordination with nearby states, temporarily accepting "regional" centralization, rather than the entire country's centralization.