0
Mathematicians
Often, to completely understand the importance of a mathematical theory, it's essential to know about the person who developed it. This category is where all questions about historically significant mathematicians should be asked.
6,570 Questions
What was it that Archimedes discovered?
He discovered that you have to find the volume, mass, and density of something
What was Eulers motivation towards maths?
He discovered the all important Euler's Rule often referred to as Euler's Formula.
What is the name of first known magnetic material?
it is the compass that people use in science for seeing directions
What is the euler's formula for octahedron?
The Euler characteristic states that V - E + F = 2
where V = vertices, E = Edges and F = Faces.
An octahedron has 8 faces, so the Euler characteristic leads to V - E + 8 = 2
or E = V + 6
An octahedron can be any one of
a heptagonal pyramid (V = 8, E = 14)
a hexagonal prism (V = 12, E = 18)
a quadrilateral dipyramid (V = 6, E = 12)
There are other octahedral shapes as well.
How do you convert repeating decimal into a fraction?
There are two methods here. The essential elements appear to be the same. Repeating decimals can be converted into fractions by the use of simultaneous equations. The trick is to identify how many numbers or decimal places are involved in the "repeating part" of the repeating decimal. Let's do one, and let's make it a familiar one. We'll take 0.3333333... which is 1/3 as you already know. First, there is only one digit that repeats. It's the 3. So we'll need to set up two equations, and the first one is that X = 0.3333333... In that equation, "X" is the decimal equivalent of the number. Now we'll create a second equation to do the simultaneous equation thing. Since there is only one digit that repeats, we're going to move the decimal one place by multiplying that whole equation by 101 which is 10. [X = 0.3333333...] x 10 = 10X = 3.333333... Notice that both sides of the equation were multiplied by 101 here. This is key. We are going to have to multiply our repeating decimal by a factor of 10 that shifts all of the repeating sequence to the left of the decimal. If we'd had 0.47474747.... for our fraction, we'd have had to multiply the equation by 102 because the "repeating part" there, which is '47' is two digits long. If it had been 0.5678567856785678.... we'd be stuck multiplying by 104 because the "repeating part" there, which is '5678' is four digits long. Back to our problem at hand. The 10 times "X" equals 10X and the 0.3333333 times 101 = 3.333333... Now we have two equations, and we're going to subject one from the other. So let's do that. 10X = 3.333333... X = 0.3333333... 10X - X = 9X, and 3.333333... - 0.3333333... = 3 Notice how the "repeating part" of the decimal "dropped out" or "disappeared" there? That's why we built two equations and subtracted one from another. We need to get the "repeating part" to get lost. Look at what's left. It this equation: 9X = 3 Can you handle that? Sure you can. Divide both sides by 9 and you'll have X = 3/9 which reduces to 1/3 and presto! Problem solved. If we'd done 0.474747474747... it would look like this: X = 0.474747474747... 100X = 47.4747474747... Note that we multiplied by a factor of 10 enough to shift a "whole block" of the repeating part to the left of the decimal. Now subtract the top equation from the bottom one. 100X = 47.4747474747... X = 0.474747474747... 100X - X = 99X and 47.47474747... - 47.4747474747... = 47 99X = 47 and X = 47/99 As 47 is a prime number, we can't reduce this fraction. There are some simple rules that apply when converting any repeating decimal to a fraction. First we'll perform the "construction" of an initial equation where we set the fraction ("X") equal to the repeating decimal. Then we'll "manufacture" a second equation from the first by multiplying the first equation by 10n where n = the number of digits in the "repeating part" of the repeating decimal so they all kick over to the left of the decimal. Then we solve the simultaneous equations, and lastly reduce our fraction. Try a few and you'll be able to slam dunk this bad boy every time you see it. This is made quite easy with the following observations:
5/9 = 0.5555
7/9 = 0.7777
12/99 = 0.121212
23/99 = 0.232323
456/999 = 0.456456456
78/999 = 078/999 = 0.078078078
So we can see that fractions with a denominator of 9, 99, 999, 9999, are pretty useful for making repeating decimals. All we have to do is to reduce the fraction to its lowest terms. For example, let's take the repeating decimal 0.027027027...
Clearly this is 27/999 = 1/37 (having divided top and bottom of the fraction by 27)
Now let's try something more tricky. Take a look at 0.4588888888...
This isn't simply something divided by 99.. since the 45 bit doesn't repeat. What we need to do is move the decimal point over to the start of the repeating bit. In this case we multiply by 100 to get 45.888888...
Now we know the fraction part is 8/9. In total we have 45 + 8/9 = 413/9 (changing into a top-heavy fraction will make things easier for us).
So 45.88888... = 413/9
Now just divide both sides by 100 to get:
0.458888... = 413/900
What is the additive inverse of -1.4?
The additive inverse of any number x is the number that, when added to x, will give an answer of 0. So for any positive number, the additive inverse is the same number, but negative, and vice versa.
So, the additive inverse of -1.4 is 1.4 since -1.4 + 1.4 = 0.
What two numbers have a sum of 45 and a product of 200?
set up a system of equations
x+y=45
xy=200
set one equal to a variable
x=-y+45
plug it into the other equation
y(-y+45)=200
distribute the y
-y2+45y=200
set it equal to 0
-y2+45y-200=0
take out the negative
-(y2-45y+200)=0
factors of 200 are 1&200, 2&100, 4&50, 5&40, 10&20
5 and 40 = 45
factor
-(y-5)(y-40)=0
solve for y
y=5,40
this is the proper way to do this or you could just guess and check
hope i helped :)
Why was Copernicus theory revolutionary?
The theory of Copernicus was revolutionary because at the time, people believed the Earth was the center of the solar system instead of the Sun.
Who is thales was he a monist or dualist?
Thales of Mileuts ~585 BC was a dualist. He taught his students of the phusis (one underlying element to everything). He believed the phusis was water. He believed in the mind and the body (as well as physical matter) being separate entities.
How did Nicolaus Copernicus study the sun?
umm well he didn't he only guessed however later on a guy called Galileo Galilei heard about a telescope and actually found out that Copernicus was correct
Who is the youngest mathematics didactics professor in the world?
Mr Andreas Ryve of Mälardalen University, Västerås and Eskilstuna, Sweden, is the youngest professor in mathematics didactics in the world.
See the related link for more information.
Who uses the Fibonacci sequence today?
The Fibonacci sequence is actually one of the most used mathematical ideas in the world! This is because the differences between the terms of the sequence give birth to the Golden Ratio (which is about 1:1.62).
This 'magic' ratio is often said to hold the key to beauty, and is found throughout the natural world - including in the ratio of sizes in a human face. Today it is most commonly used by architects, artists, fashion designers and the like - for anyone that looks to create beauty the Fibonacci Sequence and the Golden Ratio is vital because it tells you how the size you need to make things to make them visually appealing.
