Hero (Heron) of Alexandria

Hero of Alexandria

• Hero died in 70 AD. Historians do not know exactly when of how he died.

Contributions to Math

• Within his 60 years on Earth, Hero wrote a complete number of 14 works.

Formulas

Volume of a frustum

imaginary number is a number whose square is less than or equal to zero. Even though Rafael Bombelli first set down the rules for multiplication of complex numbers in 1572.

Computing the Square Root.

frustum: is the portion of a solid (normally a cone or pyramid) that lies between two parallel planes cutting it.

The volume of a conical or pyramidal frustum is the volume of the solid before slicing the apex off, minus the volume of the apex, where B1 is the area of one base, B2 is the area of the other base, and h1, h2 are the perpendicular heights from the apex to the planes of the two bases.

Newton's law states that one starts with an initial guess which is reasonably close to the true root, then the function is approximated by its tangent line (which can be computed using the tools of calculus), and one computes the x-intercept of this tangent line (which is easily done with elementary algebra). This x-intercept will typically be a better approximation to the function's root than the original guess, and the method can be iterated.

The basic idea is that if x is an overestimate to the square root of a non-negative real number S then S/x will be an underestimate and so the average of these two numbers may reasonably be expected to provide a better approximation

• The most comprehensive edition of Hero's works was published in 5 volumes in Leipzig by the publishing house Teubner in 1903.

Greek Mathematician and Engineer

Inventions

Aeolipile steam engine (hero engine) which was a rocket-like reaction engine and the first-recorded steam engine.

First ever Vending Machine! When a coin was introduced via a slot on the top of the machine, a set amount of holy water was dispensed.

windwheel operating an organ, marking the first instance of wind powering a machine in history

Heronian Mean is used in finding the volume of a frustum of a pyramid or cone. The volume is equal to the product of the height of the frustum and the Heronian mean of the areas of the opposing parallel faces.

Hero of Alexandria

10-70 A.D.

force pump was widely used in the Roman world, and one application was in a fire-engine.

Resided in the city of Alexandria in Roman Egypt. There is no recollection of of parents or even if he had a wife. he was considered the greatest experimenter of antiquity and all of his works reflected the Hellenistic scientific traditions.

• The History Channel's TV show Ancient Discoveries include recreations of Hero's inventions.

Heron's fountain A standalone fountain that operates under self-contained hydrostatic energy.

syringe-like device was described by Heron to control the delivery of air or liquids.

Heron's Formula

• His inventions have stayed with us for 1,942 years.

In geometry, Heron's (or Hero's) formula states that the area T of a triangle whose sides have lengths a, b, and c is

where s is the semiperimeter of the triangle:

photo (cc) Malte Sörensen @ flickr

• His contributions to math have enabled other mathematicians to become successful such as Newton and Bombelli.