Econstudentlog

Wikipedia articles of interest

1. Seven Bridges of Königsberg.

“The Seven Bridges of Königsberg is a historically notable problem in mathematics. Its negative resolution by Leonhard Euler in 1735 laid the foundations of graph theory and prefigured the idea of topology.

The city of Königsberg in Prussia (now Kaliningrad, Russia) was set on both sides of the Pregel River, and included two large islands which were connected to each other and the mainland by seven bridges.

The problem was to find a walk through the city that would cross each bridge once and only once. The islands could not be reached by any route other than the bridges, and every bridge must have been crossed completely every time; one could not walk halfway onto the bridge and then turn around and later cross the other half from the other side. Euler proved that the problem has no solution. There could be no non-retracing continuous curve that passed through all seven of the bridges. The difficulty was the development of a technique of analysis and of subsequent tests that established this assertion with mathematical rigor.”

2. Necessary and sufficient condition.

Somewhat basic stuff, but I just realized that if an individual has never dealt much with math or logic maybe this kind of distinction is unknown to the individual in question. I think it’s smart to go back to this kind of stuff now and again even if you know about it. Stuff like this makes it easier to evaluate arguments without spending too much time and if you haven’t dealt with it in a while, you forget stuff and make mistakes.

3. Battle of Agincourt.

“The Battle of Agincourt[a] was a major English victory against a numerically superior French army in the Hundred Years’ War. The battle occurred on Friday, 25 October 1415 (Saint Crispin’s Day, November 3 NS), near modern-day Azincourt, in northern France.[6][b] Henry V’s victory crippled France and started a new period in the war, during which Henry married the French king’s daughter and his son, Henry VI, was made heir to the throne of France” […]

“Henry, worried about the enemy launching surprise raids, and wanting his troops to remain focused, ordered all his men to spend the night before the battle in silence, with having an ear cut off the punishment for disobeying.” […]

“The field of battle was arguably the most significant factor in deciding the outcome. The recently ploughed land hemmed in by dense woodland favoured the English, both because of its narrowness, and because of the thick mud through which the French knights had to walk.[26][27] An analysis by Battlefield Detectives has looked at the crowd dynamics of the battlefield.[28] The 1,000–1,500 English men-at-arms are described as shoulder to shoulder and four deep, which implies a tight line about 250–300 men long (perhaps split in two by a central group of archers). The remainder of the field would have been filled with the longbowmen behind their palings. The French first line contained men-at-arms who had no way to outflank the English line. The French, divided into the three battles, one behind the other at their initial starting position, could not bring all their forces to bear: the initial engagement was between the English army and the first battle line of the French. When the second French battle line started their advance, the soldiers were pushed closer together and their effectiveness was reduced. Casualties in the front line from longbow arrows would also have increased the congestion, as the following men would have to walk around the fallen. […] Although the French initially pushed the English back, they became so closely packed that they are described as having trouble using their weapons properly. The French monk of St. Denis says: “Their vanguard, composed of about 5,000 men, found itself at first so tightly packed that those who were in the third rank could scarcely use their swords”,[30] and the Burgundian sources have a similar passage. In practice there was not enough room for all these men to fight, and they were unable to respond effectively when the English longbowmen joined the hand-to-hand fighting. By the time the second French line arrived, for a total of about eight thousand men (depending on the source), the crush would have been even worse. The press of men arriving from behind actually hindered those fighting at the front.

As the battle was fought on a recently ploughed field, and there had recently been heavy rain leaving it very muddy, it proved very tiring to walk through in full plate armour. The French monk of St. Denis describes the French troops as “marching through the middle of the mud where they sank up to their knees. So they were already overcome with fatigue even before they advanced against the enemy”. The deep, soft mud particularly favoured the English force because, once knocked to the ground, the heavily armoured French knights had a hard time getting back up to fight in the mêlée. Barker states that some knights, encumbered by their armour, actually drowned in their helmets.[31] Their limited mobility made them easy targets for the volleys from the English archers. The mud also increased the ability of the much more lightly armoured English archers to join in hand-to-hand fighting against the French men-at-arms. […]

Due to a lack of reliable sources it is impossible to give a precise figure for the French and English casualties. However, it is clear that though the English were outnumbered, their losses were far lower than those of the French. The French sources all give 4,000–10,000 French dead, with up to 1,600 English dead. The lowest ratio in these French sources has the French losing six times more men than the English. The English sources vary between about 1,500 and 11,000 for the French dead, with English dead put at no more than 100.[52]

Barker identifies from the available records “at least” 112 Englishmen who died in the fighting (including Edward of Norwich, 2nd Duke of York, a grandson of Edward III),[53] but this excludes the wounded. One widely used estimate puts the English casualties at 450, not an insignificant number in an army of about 8,500, but far fewer than the thousands the French lost, nearly all of whom were killed or captured. Using the lowest French estimate of their own dead of 4,000 would imply a ratio of nearly 9 to 1 in favour of the English, or over 10 to 1 if the prisoners are included.”

4. Japanese giant hornet.

“The Japanese giant hornet (Vespa mandarinia japonica), is a subspecies of the Asian giant hornet (V. mandarinia). It is a large insect and adults can be more than 4 centimetres (1.6 in) long, with a wingspan greater than 6 centimetres (2.4 in). […]

they can fly 100 kilometres (62 mi) per day and reach up to 40 kilometres per hour (25 mph) […]

In Japan, beekeepers often prefer European honey bees because they are more productive than the endemic Japanese honey bees. However, it is quite difficult to maintain a captive hive of European honey bees, as the hornets will often prey on the bees.

Once a Japanese giant hornet has located a hive of European honey bees it leaves pheromone markers around it, that within a short time attract nest mates that quickly converge on the hive. A single hornet can kill forty European honey bees in a minute and a group of 30 hornets can finish off an entire hive containing 30,000 bees in a little more than three hours. The hornets not only kill the bees, but also dismember them, leaving heads and limbs behind, to finally return to their nest with the bee thoraxes which they feed to their larvae. The hornets also gorge themselves on the bees’ honey.

The Japanese honey bee, on the other hand, has a defense against attacks of this manner. When a hornet approaches the hive to release pheromones, the bee workers emerge from their hive in an angry cloud-formation with some 500 individuals. As they form a tight ball around the hornet, the ball increases in heat [47 °C (117 °F)) from their vibrating wing forming a convection oven, as the heat released by the bees’ bodies is spread over the hornets. Because bees can survive higher temperatures (48 to 50 °C (118 to 122 °F)) than the hornet (44 to 46 °C (111 to 115 °F)), the latter dies.[1] […]

The Japanese giant hornet is large and fearsome, but it is not particularly aggressive unless it feels threatened. It has a venom which is injected from the 6.25 millimetres (0.246 in) stinger and attacks the nervous system and damages tissues of its victims. Compared to other hornet venom, it is not particularly lethal by weight (having an LD50 of 4.1 mg/kg, which compares to the deadliest wasp venom by weight of Vespa luctuosa at 1.6 mg/kg). Instead, the potency of its sting derives from the relatively large amount of venom it is able to inject with each sting.[2] Being stung is extremely painful and requires hospital treatment. On average 40 people die every year of anaphylactic shock after having been stung.[1]”

5. Haile Selassie I. “a defining figure in both Ethiopian and African history” that I’d never heard about.

August 22, 2011 - Posted by | biology, history, mathematics, wikipedia

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