Mathematics Fundamentals Quiz

Number theory, algebra, geometry, and analysis

The discovery of properties of abstract objects and the use of pure reason to prove them

A succession of applications of deductive rules to already established results

<p>Axioms</p> Signup and view all the answers

<p>Some basic properties that are considered true starting points of the theory</p> Signup and view all the answers

<p>Heron's formula gives the area of a triangle in terms of the three side lengths a, b, c. If $p = \frac{1},{2}(a + b + c)$ is the semiperimeter of the triangle, the area A is $A = \sqrt{p(p-a)(p-b)(p-c)}$.</p> Signup and view all the answers

<p>The semiperimeter of a triangle, denoted by p, is calculated as $p = \frac{a + b + c},{2}$, where a, b, and c are the lengths of the triangle's sides.</p> Signup and view all the answers

<p>The semiperimeter is $p = \frac{a + b + c},{2} = 16$, and the area is $A = \sqrt{p(p-a)(p-b)(p-c)} = 24$.</p> Signup and view all the answers

<p>Heron's formula is named after first-century engineer Heron of Alexandria (or Hero), who proved it in his work Metrica.</p> Signup and view all the answers

<p>Heron's formula, though named after Heron of Alexandria, was probably known centuries earlier and has significance as a method for calculating the area of a triangle.</p> Signup and view all the answers