Concrete patios are typically 4 inches in thickness. However, if a sidewalk supports motorized service vehicles or crosses a driveway, it may need to be as much as 8 inches in thickness.

Concrete has a significantly lower cost when compared to paving stones. On average, concrete costs about $7-$10 per square foot, while paving stones have a cost of approximately $9-$14 per square foot. It’s important to consider long-term costs in addition to upfront costs for these materials.

 
Pierre-Simon, marquis de Laplace (; French: [pj sim laplas]; 23 March 1749 5 March 1827) was a French scholar and polymath whose work was important to the development of engineering, mathematics, statistics, physics, astronomy, and philosophy. He summarized and extended the work of his predecessors in his five-volume M canique C leste (Celestial Mechanics) (1799 1825). This work translated the geometric study of classical mechanics to one based on calculus, opening up a broader range of problems. In statistics, the Bayesian interpretation of probability was developed mainly by Laplace.Laplace formulated Laplace's equation, and pioneered the Laplace transform which appears in many branches of mathematical physics, a field that he took a leading role in forming. The Laplacian differential operator, widely used in mathematics, is also named after him. He restated and developed the nebular hypothesis of the origin of the Solar System and was one of the first scientists to postulate the existence of black holes and the notion of gravitational collapse.Laplace is remembered as one of the greatest scientists of all time. Sometimes referred to as the French Newton or Newton of France, he has been described as possessing a phenomenal natural mathematical faculty superior to that of any of his contemporaries.He was Napoleon's examiner when Napoleon attended the cole Militaire in Paris in 1784.Laplace became a count of the Empire in 1806 and was named a marquis in 1817, after the Bourbon Restoration.