Category Archives: Mathematicians[post_grid id="10035"]
1. Things which are equal to the same thing are also equal to one another
2. If equals are added to equals, the whole (sums) are equal
3. If equals are subtracted from equals, the remainders (differences) are equal
4. Things that coincide with one another are equal to one another
5. The whole is greater than the part
1. It is possible to draw a straight line from any point to any point
2. It is possible to extend a finite straight line continuously in a straight line
3. It is possible to create a circle with any center and distance
4. All right angles are equal to one another
5. If a straight line falling on two straight lines makes the interior angles on the same side less than two right angles, the straight lines, if produced indefinitely, will meet on that side on which the angles are less than two right angles.
An ancient mathematician from the coastal city of Syracuse, Archimedes is largely considered one of the most prolific and most brilliant scientific minds of antiquity.
His work focused on, but was not limited to, applying the concept of infinitesimals and the method of exhaustion to prove a number of geometrical theorems.
He might have also been a super villain. I don’t know. Maybe. I’m just saying.
1. Long Range Catapults
All of the weapons that are mentioned in this article were said to have found use during the siege of Syracuse in 214 BCE.
It was the height of the Second Punic War and it was feared by the Roman Republic that the Kingdom of Syracuse might ally with their enemy, the Carthaginian Empire.
“But Archimedes had constructed artillery which could cover a whole variety of ranges, so that while the attacking ships were still at a distance he scored so many hits with his catapults and stone-throwers that he was able to cause them severe damage and harass their approach.” -Polybius (Universal Histories)
It was said that across the city wall, there were a series of holes that had been drilled through. These loopholes within the walls were said to have the breadth of a palms width. Behind these peepholes and within the city walls were stationed a number of archers with rows of the so-called “scorpions”.
A smaller catapult, or possibly a very large crossbow, the weapon discharged iron darts at the invading mariners. Deadly and impossible to counterattack, the projectile weapon would be the woe of General Marcellus. In the words of Polybius, the scorpion “put many mariners out of action”.
And if the ships still managed to out maneuver the long range artillery and the deadly “scorpions”, they still had to contend with…
“A ship was frequently lifted up to a great height in the air (a dreadful thing to behold), and was rolled to and fro, and kept swinging, until the mariners were all thrown out, when at length it was dashed against the rocks, or let fall.” -Plutarch (Parallel Lives:Marcellus)
“At last in an incredible manner he burned up the whole Roman fleet. For by tilting a kind of mirror toward the sun he concentrated the sun’s beam upon it; and owing to the thickness and smoothness of the mirror he ignited the air from this beam and kindled a great flame, the whole of which he directed upon the ships that lay at anchor in the path of the fire, until he consumed them all.” -Dio Cassius (Roman History)
Okay, you may have put your doubts aside to accept the claw of Archimedes, but surely the creation of a deadly heat ray in 200 BCE is pure myth, right?
The existence of such a weapon has been a matter of some debate over the centuries. Several scientists have attempted to recreate the machine with varying success.
The story goes that a Roman soldier came upon Archimedes in his home where the scientist was busying himself with his work. Flustered that somebody had interrupted him, Archimedes ordered the soldier to leave. The Roman either did not recognize Archimedes or realized that he was the man responsible for hundreds of Roman deaths. Either way, the story ends the same. Archimedes, now in his late eighties, was slain in his workshop by the invaders.
While Pythagoras has become known as one of the first revolutionaries in the field of philosophy and mathematics, surprisingly little is known about him, as he kept no writings of his own. All that we have learned about Pythagoras and his teachings has come to us indirectly through the writings of others.
What we do know about Pythagoras is that he was born in about 570 BCE. He visited Egypt as a young man and learned extensively about mathematical relations, proportions, and a rudimentary form of geometry. It is believed he studied within the Milesian school that had been founded by Thales a generation before. This school was devoted to uncovering the nature of the universe through objective, non mystical means; and while Pythagoras would not outright disagree with the ideas of Thales, he did take a different approach to exploring metaphysics. To Pythagoras, mathematics was the key. It was the form and order that existed in all things and through it the universe had come into being.
Pythagoras studied harmonics and learnt that much of music was governed by consistent mathematical ratios. It was said Pythagoras was given inspiration while passing a blacksmiths shop. One blacksmith had an anvil half the size of the other, and the sounds that were produced when the hammers struck were exactly an octave apart. Pythagoras experimented with musical strings and realised that there was a constant ratio between the sizes of strings that determined if they were harmonious when plucked together. This idea would become known as the harmonic series and would become very important in the fields of harmonics and even music.