EUDOXUS OF KNIDUS

Eudoxus was born in 408 BCE to an impoverished family in Knidus, Asia Minor. Because of his family’s low socioeconomic status, he would have had no chance at a successful life if it weren’t for his powerful mathematical skills. As a young adult, Eudoxus heard about Plato’s Academy and borrowed money to travel there. Many of the philosophers at the Academy ignored the young man, but Plato recognized his genius and supported him in his mathematical pursuits.

There was no remuneration for membership in the esteemed Academy, and Eudoxus had so little money that he could not afford to live with the other members in Athens. He was forced to rent a small room in the nearby city of Piraeus, where rents were low and basic food could be obtained inexpensively. He commuted daily to Athens to attend the discussions at the Academy. Eventually, after having proved several major theorems in geometry that no one had been able to tackle, Eudoxus earned the respect of the other philosophers. Thanks in part to the constant encouragement he received from Plato, Exodus surpassed all the mathematicians who came before him by devising the basic ideas of integral calculus 2,100 years prior to its formal and complete introduction by Newton and Leibniz.

Eudoxus was able to calculate volumes and areas using essentially the calculus ideas we use today. In fact, in modern mathematical analysis we use “Eudoxus sums” as part of the derivation of the integral. Unfortunately, the resulting envy of lesser mathematicians in the academy finally drove Eudoxus to leave Athens and settle in Cyzicus, where he learned and then practiced medicine. Exodus became very wealthy and was even elected a legislator.

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SHORT TRICK TO CALCULATE THE SQUARE OF ANY TWO DIGITS NUMBER THAT ENDS WITH 5.

As you probably know, the square of a number is a number multiplied by itself. For example, the square of 9 is 9 x 9 = 81. This post is made to enable you to easily calculate the square of any two-digit or three-digit (or higher) number. That method is especially simple when the number ends in 5, so let’s do that trick now. To square a two-digit number that ends in 5, you need to remember only two things. 1. The answer begins by multiplying the first digit by the next higher digit. 2. The answer ends in 25. For example, to square the number 35, we simply multiply the first digit (3) by the next higher digit (4), then attach 25. Since 3 x 4 = 12, the answer is 1225. Therefore, 35x35 = 1225. Our steps can be illustrated this way: How about the square of 85? Since 8 x 9 = 72, we immediately get 85 x 85 = 7225. Similarly we can calculate the following squares 15 x 15 = 225 25 x 25 = 625 35 x 35 = 1225 45 x 45 = 2025 55 x 55 = 3025 ...

SHORT TRICK TO MULTIPLY ANY TWO DIGITS NUMBERS.

You should observe to learn the working of this method. Step - 1: Multiply the unit digits (rightmost digits) of both the numbers, Step - 2: Add the cross product of the digits as shown below: Step - 3: Multiply the ten’s digits (leftmost digits) of both the numbers. Note: If the results obtained in step 1 and step 2 have more than one digit, note down the unit place of the result and carry over the ten’s place of the result to the left. Let us understand the process through some examples: Example 1: Solve 13 × 12 Step - 1: Multiply the unit digits (rightmost digits) of both the numbers, Step - 2: Add the cross product of the digits as shown below: Step - 3: Multiply the ten’s digits (leftmost digits) of both the numbers. So,13 × 12 = 156 Now before you get too excited, I have shown you only half of what you need to know. Suppose the problem is Example 2: Solve 28 × 35. Step- 1: Multiply the unit digits (rightmost digits) of both the numbers, Step - 2: Add the cross product of the digi...

THALES OF MILETUS

Mathematics as we know it today, with theorems and proofs, began with the great Greek mathematician Thales of Miletus (ca. 624–548 BCE). Miletus was among the first free city-states within the larger Greek empire, which spanned much of the eastern Mediterranean from Anatolia to the south of Italy and Egypt, including the islands in between. Lying on the coast of Anatolia, Miletus was one of the oldest and most prosperous Greek settlements of the time. Thales is often called the first philosopher. He is also known for his famous saying “Know thyself,” which was even engraved on the stone entrance to the cave of the Oracle of Delphi, a sacred site where the Greeks sought counsel from their gods. Additionally, Thales was one of the Seven Sages of Greece, though according to the historian Plutarch, he surpassed the others. In his book on Solon, another of the Seven Sages, Plutarch says this about Thales: “He was apparently the only one of these whose wisdom stepped, in speculation, beyo...

MAXZONE ACADEMY

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