What are some great examples of coincidence?
When I was around 10-12 years old my mom pushed me to take Chinese classes during the weekend. She enrolled me into this one small school that had about 6-10 kids per class. I became good friends with a girl named Jen (who was a year younger). After 2 or so years that school closed down and I never had a second thought about the people or the school (yay free weekends!). Fast forward 2 years. I transfer from a private middle school to a public high school outside my local neighborhood. Found out Jen goes to that school! A year later Jen transfers out to a magnet high school. Fast forward 5 years. I'm a sophomore in college in a diff city ... Find out that Jen will be attending the same college as me! We finally keep in touch a little more (keep in mind we did not keep in touch inbetween all the fallouts). One year later we decide to sign up for Chinese class together (like old times, also for GE sake). One weekend we both ended up traveling back home but separately (we're from the same city - Los Angeles). She left to go back to college (San Diego ~2 hr drive) early and realized she forgot her laptop charger! She calls me up and asks if I'm still in LA. I was. She asks if her mom can drop off the charger for me to bring back. I said yes and gave her my address. My mom being the social Chinese parent she is, was interested in meeting a fellow Chinese friend's parent. Mom comes out with me to greet Jen's mom. Turns out they were close coworkers from over two decades ago. They lost contact after Jen's mom left the company (~18 years ago). A month later Jen gives me a picture (from her mom) of us playing together as toddlers... Apparently my mom donated all my baby clothes to Jen and was even there when her mom gave birth to her.
Why is it pure happy coincidence that the area of a 3 4 5 triangle is 6?
Curiously, I thought "does this extend to any other triangle whose sides are three consecutive numbers?".Let the sides of a triangle be of length [math](x-1), x[/math] and [math](x+1)[/math]. Then this triangle has area[math]\dfrac{x}{4}\sqrt{3(x^2-4)}.[/math]This can be proved using the formula [math]\sqrt{s(s-a)(s-b)(s-c)}[/math] for the area of a triangle having the three sides [math]a, b, c[/math], where [math]s[/math] is the semiperimeter [math]\dfrac{a+b+c}{2}[/math]. This is called Heron's formula.So we need to solve the equation[math]\dfrac{x}{4}\sqrt{3(x^2-4)} = x+2[/math][math]3x^2(x^2-4)=(4(x+2))^2[/math][math]3x^4-12x^2 = 16x^2+64x+64[/math][math]3x^4-28x^2-64x-64=0[/math][math](x+2)(x-4)(3x^2+6x+8) = 0[/math]Thus, the only real solutions are [math]x=-2[/math] or [math]x=4[/math], since the quadratic [math]3x^2+6x+8[/math] does not have any real roots. However, the sides of a triangle must have a positive length, of course, so [math]x=-2[/math] is dismissed. Thus [math]x=4[/math] is the only solution, which is associated with the triangle whose sides are [math]3, 4, 5[/math].I don't know if this is a 'pure, happy coincidence' or not, but, for all it's worth, I have just proved that the only triangle whose side lengths are three consecutive numbers and whose area is equal to one more than its longest side is the [math]3, 4, 5[/math] triangle - which happens to be right-angled.(Indeed, the only right-angled triangle whose side lengths are three consecutive numbers is the [math]3, 4, 5[/math] triangle too. This can be shown by working out the solutions of the equation [math](x-1)^2+x^2=(x+1)^2[/math], noting that they are [math]x=0[/math] and [math]x=4[/math], the first of which is dismissed.)
What are some of the most interesting mathematical coincidences?
A Knight's tour across the chess board results in an amazing magic square!A knight's tour is a sequence of moves of a knight on a chessboard such that the knight visits every square only once.Now, famous mathematician Leonhard Euler came up with this awesome knight's tour:The numbers on the square indicate the number of steps taken by the knight on landing on that square. For example - the square with number 1 is the square where the tour started and the square with number 64 is the one where the tour ended. The square with number 23 is the square the knight lands on after 22 steps!So what's so special about this square?This square is a magic square where all the rows and columns add up to 260 !!And it doesn't end there! Each of the 16 half rows and 16 half columns add up to 130 !Extending this, if we cut the square by two lines connecting the mid points of opposite sides, then all the 4 smaller squares formed are magic squares with each row and column adding up to 130 !!A knight's tour ending up in such an awesome square!! This indeed is an amazing coincidence!Edit : If you divide the square further into 16 2x2 squares, then the numbers in each of these squares add up to 130Thank you for the observation Diana Crețu
Predict whether an aqueous solution would be acidic, basic or neutral?
Here's a sure-fire way I give my students to predict if a salt is acidic, basic or neutral What we're looking at is "hydrolysis", the reaction of a salt with water. You must know the strong acids and bases in order to use the system. Strong acids: HCl, HBr, HI, HNO3, HClO4, H2SO4 (1st H only) Strong bases: Group IA hydroxides (not HOH) and Ca(OH)2, Sr(OH)2, and Ba(OH)2 Here's the system: Look at the cation and anion of the salt. 1. If the cation comes from a strong base, and the anion comes from a strong acid, the salt will be neutral. 2. If the cation comes from a strong base, and the anion comes from a weak acid, the salt will be basic. 3. If the cation comes from a weak base and the anion comes from a strong acid, the salt will be acidic 4. if the cation and ion both come from weak acids and bases, it is impossible to predict. You must know the relative strengths of the acid and base. Using this system: 1.sodium nitrate NaNO3 - neutral 2.ammonium iodide NH4I - acidic 3.sodium bicarbonate NaHCO3 - basic 4.ammonium cyanide NH4CN - can't tell* 5.sodium hypochlorite NaOCl - basic 6.potassium acetate KCH3CO2 - basic * can't tell unless you look up the relative strengths, which are almost the same, so this solution is essentially neutral.
Doesn't it seem too coincidental that the moon is at the exact distance required between the Earth and the Sun to create eclipses?
First off, I'm not certain this is a valid question, so I'm going to do some math:The suns diameter is 864,948.7 milesThe distance of the Earth from the sun is 92.96 million milesSo we get the following equation: 864,948.7 x 108 = 92.96 million*Uses Calculator*When in reality, the equation is 864,948.7 x 108 = 93.41 millionso the distance between the sun and earth is not the suns diameter times 108, it is the suns diameter times 107.4. But that is still extremely close, so lets try the moon part of the question.Diameter of the moon: 2,159 milesAverage distance from earth: 238,900 miles*Uses Calculator*Once again using the same equation as before, we get that the diameter of the moon times 108 is 233,172, not 238,900. The moon's diameter times 110.6 is the distance between the moon and earth.Now since I'm doing the math already, might as well debunk or prove another 108 theory, that the diameter of the sun is 108 times the diameter of Earth.Diameter of sun: 864,948.7 milesDiameter of earth: 7,917.5 milesAnd again 7,917.5 times 108 should equal 864,948.7.*Uses Calculator*Nope, earth's diameter times 108 equals 855,090, not 864,948.7. Earth's diameter times 109.2 is 864,941.7 though.So, as you can see by the results, all of the actual numbers are different, granted that 107, 110, and 109 are extremely close, in reality, they each represent a larger number that is hundreds of miles of the point it should be if everything was 108. The fact that these numbers are so close though is pure coincidence, nothing to keep you up at night. Oh, and I'm sorry for the math lesson!
What exactly is the 23 Enigma, and why are so many people obsessed with it?
Jim Carrey was already obsessed with the number 23 before he got the script for his upcoming thriller, Number 23, so when he saw it he was very eager to be a part of the project. In fact, he’s so obsessed that his production company is called JC23. But he is not alone; the number 23 has puzzled and captivated millions across the globe for many years. Just type number 23 or 23 enigma into your browser and see what people have to say about it. But be wary, while some sites glorify the magic of the number (Alexander the Great cut the Gordian Knot at age 23, Adam and Eve are said to have had 23 children), others reveal the dark curse of it (2/3 is .666, the Mayans believe the world will end on December 23, 2012).
What do you say when someone asks you why u believe in God?
I'm Catholic. What do you say when someone asks you why you believe in God? When asked this question, I replied ," life is too amazing to be a coincidence " To which the 'questioner' said ," that doesn't mean God created it, there is evidence other wise" So I said , "explain miracles" And they said,"that's ignorant, you're saying you have no idea how it happens so it must be a god. & give 1 example of a miracle" I said next, "why are u so head strong? I believe in God& I answered your question. My mind will not be changed & you are only strengthening my faith" I am somewhat angry now. I understand not everyone believes & I accept that. But it makes me upset when someone can't accept my life. I really want to say something strong and thoughtful, yet I'm not sure what to say. Does anybody have something good to say? I love God but this is a somewhat... tricky question to answer. I know what I think but it can't be put into words. Anyone have something that actually makes sense to say? Thanks so much. 10 easy points xx
Is This True About Hallow'een, Easter and Christmas? And Should We Celebrate Them?
All Saints day is not the same for all Chritians, the Orthodox Church celebrates it the sunday after Pentocost. The western all saints day was selected by Saint Patrick as it was the Celtic new year. I still celebrate the western Haloween as I am of celtic decent and Patrick is my Patron saint, and costumes are cool. Easter is not the Greek name in the countries that tradtionaly folloe ther Orthodox Church some variation of Paskha is used. Paskha also means passover the original calculations of the date were designed so it would be some sunday after the Jewish passover- it changed in the west during the medival/renesace period. Eggs have always represtended life. Christmas- there are litugical reasons for the date as well. manly the early church would fast for 40 days before both feasts. (eastern Christians still do) so it was set up to give some spacing between the two feats. Christmas is actualy a period of 2 feasts the nativity Decemebr 25th and the Epiphany- Janurary 6th. We have a better idea of when the redurection was then the nativity as there is no clear date given. As for paganism it is important to remeber what ever date you choose you could find some pagan celebration about the same time and some costoms would carry over. For example in part of Europe there is a folk dance in many viliges on Easter sunday which stems from pagan spring festavals. These things would have some of their meanings changed as it would now be about having fun while celebrating Christ.