When can YOU do this? Under what circumstances can you multiply swiftly? Do you ever make a (let us all pause here) geometric illustration of your calculation in your head? Can you picture something with, say, algebra tiles? Let me illustrate.
Let the following illustration of a rectangle represent the product of 43 and 42. Let the horizontal represent 40+3 and the vertical represent 40+2. The blue square represents 40x40; the green bars each have dimension 1 x 40; the yellow squares each represent a 1 x 1 unit.
...or how the tiles support FOILing:
But there's more. I'd like to draw your attention to two modern-day mathematical geniuses from India.
One woman, Shakuntala Devi is known as "The Human Calculator" for her ability to calculate products of large numbers in her head very swiftly. From the on-line version of the India Times:
Shakuntala Devi once competed against a computer to see who could come up with the cube root of a 9 digit number first and she defeated the computer at this challenge. The same year, in 1977, Shakuntala Devi was asked to give the 23rd root of a 201-digit number; she answered in 50 seconds! On June 18, 1980, she demonstrated the multiplication of two 13-digit numbers 7,686,369,774,870 × 2,465,099,745,779 picked at random by the Computer Department of Imperial College. The correct answer was presented by her in just 28 seconds!
I've always loved stories of Srinivasa Ramanujan. One of my favorite stories is the following, from Durango Bill's site:
If you mention the number “1729” or the phrase “Taxicab Problem” to any mathematician, it will immediately bring up the subject of the self-taught Indian mathematical genius Srinivasa Ramanujan. When Ramanujan was dying of tuberculosis in a hospital, G. H. Hardy would frequently visit him. It was on one of these visits that the following occurred according to C. P. Snow.
“Hardy used to visit him, as he lay dying in hospital at Putney. It was on one of those visits that there happened the incident of the taxicab number. Hardy had gone out to Putney by taxi, as usual his chosen method of conveyance. He went into the room where Ramanujan was lying. Hardy, always inept about introducing a conversation, said, probably without a greeting, and certainly as his first remark: ‘I thought the number of my taxicab was 1729. It seemed to me rather a dull number.’ To which Ramanujan replied: ‘No, Hardy! No, Hardy! It is a very interesting number. It is the smallest number expressible as the sum of two cubes in two different ways.’”
A second option for your blog this time is to search the web for yet another "human calculator." Have your mathematician be from relatively modern times (the last 100 years) and write something about him or her. Include your internet sources in your blog.
A third option for your blog this time is to find an interesting story about one of these two folks that I identified above that are NOT on the sites I've provided for you. Also be sure to include your internet sources in your blog.
I decided to research about Shakuntala Devi. One story that I found in multiple places was about her childhood. Her father was a circus performer and when she was only 3 he discovered her abilities for math. He recruited her to help with his card tricks. I was curious as to how her math skills helped with card tricks so I decided to look into that further. On this website :http://www.firstpost.com/living/my-meeting-with-temperamental-math-genius-shakuntala-devi-717760.html I discovered that she also had a photographic memory. She memorized the order of the cards in the deck, then was able to guess a card. Also as part of her father's circus, she performed math problems in her head quickly. This was the beginning of her lifelong fame and performances as the "human calculator".
ReplyDeleteOne other interesting tidbit that I learned was how much Devi saw math in her everyday life. This is expected of a mathematician, but I thought it was interesting to the extent that she saw math in our world. Besides seeing math in flowers and hearing it in birds chirping, she saw it on license plates. This website: http://articles.latimes.com/1988-03-01/news/mn-328_1_201-digit-number talks about how she would see a number on a license plate, then play with it. For example, when she saw the number 720 she came up with this: 1 x 2 x 3 x 4 x 5 x 6 equals 720.
Hello, again! I have recently discovered a man, named Scott Flansburg, who holds a Guinness World Record for being able to calculate faster than a calculator in adding the same number over and over again as many times as he can in 15 seconds. He beat the calculator by adding 38 thirty-six times in a row.
ReplyDeleteHe has these very cool ways of teaching how to add, divide, and multiply numbers. He claims that around the world we teach math in a manner that requires so much memorization that math doesn't useful or user friendly. He claims that every day of your life you will have to use numbers at some point, no matter what you are doing. He also claims that his ways of teaching simple maths skills will make people feel more comfortable dealing with numbers, and make numbers easier to understand and deal with. He says that numbers are confusing because use them in the completely incorrect way. We add in the opposite direction as we read and we have to memorize everything. We make maths harder than they really are and he has found the easier routes to understanding numbers.
Here are a few videos that talk about what he does!
http://www.youtube.com/watch?feature=player_embedded&v=nTpLpOZXnUI
http://www.youtube.com/watch?feature=player_embedded&v=vGULqoEP5TE
Sources
http://scottflansburg.com/
www.youtube.com
www.google.com
42x43
ReplyDeleteThe area of a region is the sum of the areas of its non-overlapping parts. How can we use this postulate to demonstrate that this block illustrates the traditional way to multiply 42 by 43? The blue block has dimensions of 40 by 40, making it a square. The green blocks below the 40x40 block are the dimensions 40x1, as are the other green blocks next to the 40x40 block. The yellow blocks represent 1x1 squares. Before demonstrating how the blocks illustrate the equation, take the equation 42 x 43 and multiply it.
First multiply 2 and 3. 2x3=6
Next multiply 3 by 40. 3x40= 120
Now multiply 2 by 40. 2x40=80
Finally, multiply 40 and 40. 40x40= 1600
6+120+80+1600= 1806
This is how one would traditionally multiply 43 by 42. You would line the numbers up and multiply the top by the bottom. Now, multiply the area of the blocks. The area of a rectangle is equal to the base multiplied by the height. Taking this equation, find the areas of each block.
Yellow blocks with 1x1 dimensions: 3 blocks across x 2 blocks down= 2 x 3=6
Green blocks on right with 1x40 dimensions: 3 blocks across= 3 x 40=120
Green blocks on bottom with 1x40 dimensions: 2 blocks down= 2 x 40= 80
Blue block with 40x 40 dimension: 1 block= 40 x 40= 1600
6+120+80+1600= 1806
Multiplying 42 x 43 and calculating the area of the blocks both yield an answer of 1806. The block method even parallels the multiplication because the exact same equations are performed to find the answer. How does this work? It is important to remember that when you multiply a number, you are saying “it is this number this many times”. The blocks illustrate this idea. You take the block with 1x40 dimensions and you say “it is 1x40 three times because there are three blocks”. The dimensions of the block are 42x43 (the blue block plus two green blocks down and the blue block plus three green blocks across), but you are just dividing the area further so that you can work with more manageable numbers.
I can occasionally calculate things in my head somewhat quickly, usually only something like 40 * 43. I know 40 * 40 is 1600, so I figure that 40 * 43 is 3 more 40s, or 120; so 40 * 43 is 1720. When one number is a multiple of 10, and I can make the other into one, that makes it easier for me. Beyond that, though, I need to either write it out or use a calculator.
ReplyDelete(This is kind of a tangential comment, but I thought it would interest you: When my parents went to college, there was a nine-year-old who was taking the same math classes as they were. When you mentioned math geniuses, I thought about this, even though I guess he's more of a prodigy.)
I can see how the image you give relates to FOILing. You have the big square that's 40 * 40; the three (vertically placed) rectangles on top represent 40 * 3, the (horizontally placed) rectangles toward the bottom represent 40 * 2, and the six yellow squares represent 3 * 2. And since 42 * 43 can be represented as (40 + 2)(40 + 3), this makes it work. It also reminded me a bit of the "lattice method" that I was taught as an alternate method for multiplying. Here's a link to a description, if you're interested http://en.wikipedia.org/wiki/Lattice_method. Visually, at least, the two seem similar.
Alexis Lemaire is a French "human calculator" born in 1980 who I find particularly impressive. He holds the world records for mentally calculating the 13th root of both 100 and 200 digit numbers. I was amazed to hear that in 2007 he mentally calculated the 13th root of a random 200 digit number in just 70.2 seconds. Lemaire trains his mind the way an athlete trains his body. He practices and memorizes every day. In an interview with BBC he said, "When I think of numbers sometimes I see a movie, sometimes sentences. I can translate the numbers into words. This is very important for me. The art is to convert memory chunks into some kind of structure." To me, this seems like the most important aspect of his skill. He doesn't view numbers in the same way most people do, which allows him to calculate such incredibly high roots in his head. In addition to this, his large memory must help him out too. I think he probably has a natural talent for such things, but he has expanded his skills farther through diligent practice. Very inspiring.
ReplyDeleteSources:
http://www.csmonitor.com/Innovation/2013/1104/Shakuntala-Devi-and-other-human-calculators
http://en.wikipedia.org/wiki/Alexis_Lemaire
http://news.bbc.co.uk/1/hi/magazine/6913236.stm
Many times I like to calculate things in my head rather than get my calculator out. It takes more time to get my calculator out than it would to just calculate the equation in my head. Double digit numbers are the toughest and it takes me a longer time to figure these out than single digit or single digit and double digit multiplication or division. Addition is very simple for me to do in my head although for bigger numbers I have to take a little more time to carry numbers. When I'm doing homework I have more confidence in calculating things in my head than when I'm taking a test. It's funny because I can calculate big numbers in my head but when it comes to a test I doubt myself for the simplest equations like 2*3. I calculate everything just to make sure I don't make a mistake. I also check the calculator many times to make sure I typed in the right numbers.
ReplyDeleteThese tiles support FOILing because the blue rectangles has a 40*40 dimension and the three small rectangles have dimensions of 1*40 therefore the side of the larger rectangle is 40+3, and the other side is 40+2 because their is the 40*40 rectangle and only 2 1*40 rectangles. The area of the larger rectangle is (40+2)(40+3).
Scott Flansburg, an american dubbed "the human calculator" always tells people that he is "not an athlete, but a mathlete" (Discover Channel-More than Human). When invited to speak on the Oprah Winfrey show, he did a series of warm up exercises before going out on stage much like athletes do before every game and practice. He exercised his mind before the show by adding numbers, multiplying two digit numbers and doing long division in his head. In this Youtube site http://www.youtube.com/watch?v=YGFi-XswpoI, Scott shows his amazing ability to multiply two digit and three digit numbers unbelievably fast. He starts off with a 3 digit number like 373 and adds 373 to itself consecutively and keeps doing it even when he has reached well into the 6-7 digit numbers. His world record is from adding the same number to itself 37 times in 15 seconds (Guinness Book of world Records). It's astounding. He says that he doesn't count from 1 to 10. Instead he counts from 0 to 9. As he astutely mentions, everything relates back to 9. Take 11 for example. The two digits in 11 are 1 and 1. Add them together and they make 2. 11-2 is 9. Try it for 13. It works as well. He says that counting as if 9 was the highest number instead of 10 makes it so much easier. Take the number 55 for example. The two digits in 55 are 5 and 5. 5+5 = 10. 55-10= 45. 4+5 is 9. He says that if you don't get 9 in the end it means you've messed up. Every number problem relates to 9. It's just another way to check if you're right or not.
ReplyDeleteThis is his website: http://scottflansburg.com/
Alexis Lemaire is a world famous mathlete. His task was to find the 13th root of 85,877,066,894,718,045,
ReplyDelete602,549,144,850,158,599,202,771,247,748,960,878,023,151,
390,314,284,284,465,842,798,373,290,242,826,571,823,153,
045,030,300,932,591,615,405,929,429,773,640,895,967,991,
430,381,763,526,613,357,308,674,592,650,724,521,841,103,
664,923,661,204,223with the answer being 2396232838850303 that he calculated in under 77.99 seconds, breaking his own previous record. When asked about his incredible ability, Lemaire responded saying, "It is quite difficult. I did a lot of preparation for this. More than four years of work and a lot of training every day. A lot of memorising. I need three things - calculating, memorising and the third on mathematical skills. It is a lot of work and maybe a natural gift" (http://news.bbc.co.uk/2/hi/uk_news/magazine/6913236.stm). So how does he do it? Lemaire talks about being able to transform number into structure or shapes to "see" the answer to the problem, "I see images, phrases, actions. It's very tactile, sensitive. I have these associations between places and numbers - some places are imaginary, I try to vary so I don't confuse the numbers" He can also think of numbers and see movies or sentense. He calls it "translating numbers to words" (http://news.bbc.co.uk/2/hi/uk_news/magazine/6913236.stm). It is truely amazing how our brains work sometimes!
During the Summer, while writing a paper for my Biology class, I stumbled on the amazing and incredible story of Daniel Tammet. Daniel is an individual who has a spectrum disorder (autism, etc.) called Savant Syndrome, (also the topic of my paper,) a really interesting and mysterious mental disability that has still yet to be fully researched. While in most cases, this ailment leaves the individual very inept socially and physically, Daniel is a rare exception to the handful of individuals, (less than 100 in the world,) who is capable of communicating and conversing socially with other people.
ReplyDeleteThe whole disorder starts in the brain, where due to trauma or genetic pre-disposition, the brain of an individual with Savant Syndrome is very different than that of you or I. In the brain, many different lobes and cortexes are larger or smaller than the normal size, leading to mostly detrimental effects on their functioning, but at the same time rare cases where it can be advantageous. This deviation in lobe and cortex size in an individual with Savant Syndrome occurs namely in the areas of the Hippocampus (the memory center of the brain,) and the Corpus Callosum (the memory filter in the brain). Due to this abnormality, individuals with Savant Syndrome have a much larger area to store memory, and because there is no filter, their habitual memory, (daily events, senses, interactions, information learned,) is retained in a much larger quantity of that stored in a normal human brain. For example, the normal human brain can retain about 40-50% of the information absorbed unintentionally, through senses, interactions, etc. An individual with Savant Syndrome though, can retain close to 98% of the information they absorb daily.
There are many different areas of ability that Savants area in, but Daniels seems to be able to connect with languages and math the best. Due to his condition, Daniel Tammet was able to recite 22,514 digits of the number Pi in 5 hours, and 9 minutes with no flaws. His method seems to be that to him, each number and letter has a color, texture, and shape, and to remember something, he simply has to create an environment from these figures. When reciting Pi, Daniel said that all he had to do was walk through his “mind environment” and see the numbers that made up the picture.
Here is the documentary that shows Daniel reciting 22,514 digits of Pi!
http://www.tubechop.com/watch/1647058
Scott Flansburg hold the Guinness World Record for the "Human Calculator". Flansburg has been teaching for more than 20 years. He is able to subtract, add, multiply, take the square and cube roots of numbers in a short amount of time. He said the only that holds him back is that he cannot speak as fast as he gets the answer. I think it is really interesting that he can do math in his head faster than professionals on calculators. He has appeared on many talk shows such as Oprah, The Ellen DeGeneres Show and ABC’s Good Morning America.
ReplyDeleteThe Human Calculator reminds me of when I was watching Live! with Kelly and Michael when a teen came onto the show. He was wearing a math Olympiad shirt and he solved mathematical questions against Kelly and Michael. he answers the questions way faster than than the two hosts. The questions aren't as complicated and complex as the ones Scott Flansburg does, but he is still impressive. I am unable to find a link or video on him. I just remember sitting on the couch with my mom trying to see how fast I could solve the problems.
The Human Calculator also reminds me of when I was in about 4th grade we did a race against another student on a calculator. It was simple multiplication to 12 x 12. Almost all the students were faster than the calculator. Once you commit the math to memory it becomes easier and faster to yourself.
Sources:
http://scottflansburg.com/
I decided to read up on Wim Klein. Klein worked as a physicist at CERN from 1958- 1976. He is considered to be one of the world's first human calculators. He worked at CERN at a time when there weren't many computers and because of this the scientists there greatly appreciated his ability to calculate calculations that may have taken much longer to complete without his help. Even the computers back then couldn't keep up with his calculations. When the computer eventually did become much smarter and faster it became Klein's job to make the equations inserted into the computer much simpler for it to read. He was an inspiration to future human calculators and will always be remembered as one of the best.
ReplyDeleteI calculate things really fast sometimes like this, but I don't think I could multiply three or four two digit numbers together in my head! Sometimes when my family and I are playing a bored game together and we have finished the game and are tallying scores I already know who won. It takes time for each person to individually add up their own score, but for me it's simple. My dad tells me to be quiet sometimes as I blurt out the scores and winner of each game we play. Maybe someday I will be able to multiply numbers like Klein.... but not today!
Source:
http://www.symmetrymagazine.org/article/december-2012/%E2%80%98human-calculator%E2%80%99-wim-klein-advanced-physics-inspired-others
For my blog, I watched the video of Shakuntula Devi being interviewed on RT, a Russian news show. In the interview, she said that she first discovered her natural ability and her love for math when she was only three years-old. This brings me to my question. Are geniuses born with their gifts? In my opinion, their is a combination of work and natural gifts. I believe that if someone loves something and works really hard at it, they are able to become masters at it. On the other hand, you have to naturally love what it is you are studying or else you will never be motivated to do anything.
ReplyDeleteIn some instances I have performed fast calculations. I don't normally like to when calculation random things, but when there is a formula to follow, I can normally do it. In science, when you are performing the same calculations constantly, it is really helpful to use fast calculations.
RT video: https://www.youtube.com/watch?v=wU_FDnLFU9A
The "human calculator" I researched about is Scott Flansburg. On his website, he talks about how he received the name from Regis Philbin and has been called "The Human Calculator" ever since. He teaches math, does talk shows, and is also a best selling author of his book "Turn on the Human Calculator in You". People will challenge Scott with complicated math problems to which he can spit the answer out in under a minute. He added the same number to itself more than 15 times and hold the Guinness World Record for the "fastest Human Calculator". He even claims he would be faster than that. but he can't speak the answers as fast as he can calculate them in his head! Scott Flansburg has appeared on many talk shows and gives interviews around the world to spread his love of math. I watched a cool video on Scott's new teaching method of simple addition for kids elementary school. Instead of adding up the ones column numbers and carrying the tens digit to the tens column, Scott teaches us to start by adding up the tens digit numbers and then move to the ones column and add each of those to the previous number. An example could be 47 + 57 + 21. We start by adding the tens digit numbers. 40 + 50 + 20 = 110. We then add the ones digit numbers 7, 7, and 1. 110 + 7 = 117. 117 + 7 = 124. Finally, 124 + 1 = 125. he claims it is much easier for children because of the way we read left to right and that the idea of carrying the ten is confusing for children and just encourages useless memorization of adding techniques rather then learning to add two and one digit numbers simpler and faster. I agree with him and I even tested it to and could add simple numbers much faster than I could with the traditional method. Scott's dream is to teach this to kids starting in North America and start a revolution allover the world changing how we learn simple math from the beginning.
ReplyDeleteGA2 The Human Calculator
ReplyDeleteScott Flansburg, nicknamed the Human Calculator by Regis Philbin, believes the ability to excel at math and enjoy it is available to everyone; he also believes that most people, who dislike math, have not learned math in a way that works well for them. Scott holds the Guinness World Record holder for "Fastest Human Calculator," due to his ability to add in fifteen seconds the same number to itself more times than a person with a calculator. Daily, he is challenged with large math problems and able to answer each just by using his head! His astonishing math skills allow him to add, subtract, multiply, divide, and find square and cube roots of numbers with accuracy and speed in his head. Scott Flansburg, a best selling author, has written "Math Magic" and "Math Magic for Kids." In his twenty years of teaching, Flansburg strives to help people of all ages improve their basic math skills and to convince people that math is fun. Over these years Scott Flansburg has appeared on several talk shows such as The Tonight Show with Jay Leno, The Ellen Degeneres show, Primetime America, USA Today Radio Network, Dateline NBC, and many more talk shows. Scott Flansburg teaches math and entertains people with his amazing mathematical skills.
http://scottflansburg.com/meet-scott/
While doing mental math it is very easy to split up the equation especially during multiplication. Just like it is shown above with 42x43 you can take 40x43 then just add 2x43. These can be done very easily since they are either smaller numbers or numbers that are easy to multiply with. This could be related to area because while finding area with large measurements, you can split up the shape to make it easier. Especially when you have abstract shapes you are forced to split it up into multiple areas and you try to find ways to split it to make it easier to find the areas. Both of these tricks require you to have a visual image of the math in your head. While splitting up a multiplication problem I try and keep the products in my head like i was writing it down on a piece of paper. This makes it easier for me to the line up the products when it is time to add them all together. Same with splitting up areas you have to be able to see the smaller shapes within the large abstract shape while still understanding that you'll need to put it all back together again. If you aren't able to do this it becomes very hard to store the numbers in your head making it harder to piece it all back together.
ReplyDeleteThe figure above demonstrates a quicker and easier way to multiply numbers in your head. To do the calculation 43x42 in your head is very difficult especially if you do not think about it and you try to do long multiplication in your head. To better complete this task of multiplying, we can multiply groups of easier numbers in our head that add up to the same value of 43x42. For me personally, I would not have the rectangle with all of the colors in it in my head, but it shows the principle.
ReplyDeleteWe have above one 40x40 blue square, 5 green 1x40 rectangles, and 6 1x1 yellow squares. So knowing this information, we can derive the 43x42 calculation much easier.
The first thing we will do is multiply the area of each different colored squares and rectangles.
The area for the blue square, 40x40, is 1600.
The area for each green rectangle, 40x1, is 40
The area for each yellow square, 1x1, is 1
Now that we have the areas, we have to multiply each value by the number of the respective shape that is in the figure.
For the blue square 1600x1=1600
Green: 40x5=200
Yellow: 1x6=6
Now that we have the areas of each color in the figure, we can add them together to get the area of the whole figure, and consequently, it will be the value of 42x43 because those are the sides of the figure.
We add 1600+200+6 to get our answer of 1806, which in fact is the result of 43x42.
There are other human calculators outside of India. Alexis Lemaire, a Frenchman, who was born in 1980 can do some insane math as well. He can calculate the 13th root of say85,877,066,894,718,045,602,549,144,850,158,599,202,771,247,748,960,878,023,151,390,314,284,284,465,842,798,373,290,242,826,571,823,153,045,030,300,932,591,615,405,929,429,773,640,895,967,991,430,381,763,526,613,357,308,674,592,650,724,521,841,103,664,923,661,204,223 faster in his head than he could using a calculator.
ReplyDeleteIt takes him a remarkable 80 seconds and he won a world record in 2004 for doing it. I think that really incredible because think how fast he could find the root of say 2. He doesn't use geometric illustrations but instead sees the numbers as a story- filmed or written. He practices daily to be able to retain his ability. I'm really curious as to if this skill, being a human calculator, is learned or if it's just natural. He fitting majored in artificial intelligence ( "the science and engineering of making intelligent machines"); this isn't a handy skill for an English major. According to the Wikipedia page on metal calculation, the skill can be learned or be natural, some people with autism can show great or supernatural strengths in one or two mental pursuits but have no capacity in others.
http://www.csmonitor.com/Innovation/2013/1104/Shakuntala-Devi-and-other-human-calculators
http://en.wikipedia.org/wiki/Artificial_intelligence
http://en.wikipedia.org/wiki/Human_Calculator
The famous mathematician or "human calculator" that I researched is Alberto Coto Garcia. He was born in Spain in 1970 and is now recognized by the Guinness Book of World Records as the fastest human calculator on the planet. When Alberto was six years old he began to develop his skills in calculating by counting the different scores one could get when playing cards. Throughout his life he has constantly practiced and refined his skills in speed calculations and now holds seven championship titles in speed addition, multiplication, and mental calculation. His most impressive accomplishment is that he holds the world record for adding 100 random digits. He was able to correctly complete these operations in 19.23 seconds, the fastest time ever recorded. To be able to be able to add 100 digits in 19 seconds, Alberto had to average 5 operations per second, meaning that every second he added five digits together, remembered them, and then added them to even more digits. He has also written three books about his calculation skills and how to improve memory and your mind. All three of his books have been acclaimed best sellers in both Latin America and Spain.
ReplyDeleteSources:
http://roadtickle.com/amazing-human-calculators/2/
http://en.wikipedia.org/wiki/Alberto_Coto_Garc%C3%ADa
Mike Byster, an american mathematician, has an aptitude for calculating numbers mentally and determining patterns of numbers and words. He worked as a stockbroker before quitting his job and devoting his time to teaching kids his methods and abilities. He’s the creator of Brainetics, a website that exercises math and memory skills. According to psychologists Byster is said to be one of the fastest mathematician in the world. He’s able to solve complex problems at an incredibly fast speed, such as 999 divided by 56.
ReplyDeleteByster stood out to me because instead of keeping his talent to himself and using it to solve unsolved math problems he teaches others. He inspires
people of all ages to improve their math and memory skills. This is significant because instead of taking his talents with him to the grave he is spreading his knowledge to the general population, and possibly creating many future mathematicians. I respect what he has done with his talents.
Alexis Lemaire is a french mathematician that was born in 1980, and has the ability to do some incredible math in his head. One famous example of his incredible ability was shown in 2007 when he calculated the 13th root of a random 200 digit number in just over 70 seconds. He hones his skills by practicing everyday, at first he started by finding the 13th root of 100 digit number then wen that became too easy he moved on to a 200 digit number. This is really incredible, there are few people who can do very complicated equations in their heads in short periods of time. It seems to me that it goes one way or the other. What i mean is that a person is able to calculate extremely complex equations in their mind at super fast speeds, or they take awhile and are not able to do the math in their heads. One thing that i find interesting that ties in with this a little i saw in the movie Rain man with Tom Cruise and Dustin Hoffman, where Hoffman is Tom Cruise's older autistic brother. Hoffman has troubles in everyday life and doesn't really comprehend the easy things like making toast and using a toaster. He has an incredible memory, and the ability to calculate incredible numbers at lightning speed. Many of todays human computers, or calculators are not autistic, it makes you wonder what someone who is could be capable of and what the human mind can really do.
ReplyDeletehttp://en.wikipedia.org/wiki/Alexis_Lemaire
http://www.csmonitor.com/Innovation/2013/1104/Shakuntala-Devi-and-other-human-calculators
http://www.worldrecordacademy.com/human/Fastest_Human_Calculator_world_record_set_by_Alexis_Lemaire_70946.htm
Another human calculator that I came across was a Guinness World Record holder named Scott Flansburg. Flansburg achieved this world record by adding the same number to itself over and over again more times in 15 seconds than a calculator could. He often appears on talk shows and advocates a new method of teaching young children basic arithmetic. His new idea involves doing away with the old method of carrying the tens over when adding and instead starting on the left side of the problem and adding the tens place together first, then moving on to the ones place. He has written several books on this topic, hoping to revolutionize this method. Flansburg counts differently than the rest of us; on his fingers he starts with zero and goes to nine instead of 1-10. This helps him while he does speedy calculations; he starts himself at zero like a calculator would. Based on this Flansburg has also come up with a new calendar that uses zero as a month and goes to 13 months instead of 12. In general, I believe that Flansburg has some very interesting and creative ideas to try to transform the way we do math today; however, it seems that because his way of thinking is very different than most people it will be difficult for the majority to change to his ways. This difference in thinking is not a bad trait; it is what allows Flansburg to be great and incredibly talented in math calculations, it just seems to create a kind of barrier between his thought processes and the rest of the world.
ReplyDeletehttp://scottflansburg.com/#
http://en.wikipedia.org/wiki/Scott_Flansburg
Arthur Benjamin is one "human calculator" that i have actually watched over the years. I can't remember exactly, but my parents bought a series of videos called the "great courses" made by Arthur. They bought these videos to help my brother in his math class. This is when i first saw him. I then later saw him on some TED videos. http://www.youtube.com/watch?v=e4PTvXtz4GM. In these videos he demonstrates his insane ability to calculate huge multiplication problems. He calls his form of math "mathemagic." In these TED videos he usually asks his audience to give him a number with a certain number of digits. He then asks for another number with a certain number of digits and he is able to perform the multiplication of the numbers much faster than a calculator could. He also takes the square roots of up to 5 digit numbers and thinks out loud as he calculates the answer. Until he is asked to calculate numbers above 4 digits, Arthur always beats a calculator. Arthur also shows off in this particular TED video by demonstrating his knowledge on birthdays. He asks the audience for their birthdate and is able to give them the exact day of the week they were born. He takes his knowledge to another level by asking a volunteer to give him a random date between 1600 and 3000 (future). The volunteer gives the date 2730 on June 13; Arthur tells him that that will be a friday within 3 seconds. He probably is not the most famous mathematician. But Arthur Benjamin certainly blows my mind apart. He has a lot of videos on youtube where he provides math tricks that we can use in our every day life. http://www.youtube.com/watch?v=ZvzsWmUqDF4.
ReplyDeleteArthur Benjamin has been a professor at Harvey Mudd College since 1989. He is my favorite mathematician because he is so knowledgeable and also provides a lot of math help. He really helped my brother out in calculus and i hope i still have his tapes because he is a very good teacher. EUS!
http://en.wikipedia.org/wiki/Arthur_T._Benjamin
Wim Klein, a human calculator, was a Dutch mathematician capable of solving very tough problems in his head. He was able to earn a spot in the Guinness Book of World Records by taking two minutes and 43 seconds to calculate the 73rd root of a 500-digit number. He worked at CERN Laboratories from 1958 to 1976, and he completed difficult calculations for physicists which otherwise may have taken very long to solve. Once computers became more advanced, Klein's job turned into simplifying numerical problems which would then be fed in a computer. Klein spent hundreds of hours memorizing multiplication tables, and as Fountain, another human computer says, "I could see it was no trick-it was a skill, and therefore something I could learn to do myself."
ReplyDeleteThis struck me. I wonder if becoming a human calculator really is possible to anyone who puts in the work and effort, or if it is something you are just naturally gifted in.
http://www.symmetrymagazine.org/article/december-2012/‘human-calculator’-wim-klein-advanced-physics-inspired-others
Alexis Lemaire was declared the faster human calculator when he took the 13th root of a 200 digit number in his head in 70.2 seconds. This was the world record and Alexis was very proud of himself. The first 200 digit number that he tried to 13th root took him 40 minutes to complete in his head. He then put himself through many training exercises to repeatedly cut his time. When asked, Alexis would not give away his secret but he did say that it was not all about math. It was also a lot of memorization. Daily Mail challenged Alexis with a 30 second challenge that he completed, in 8 seconds.
ReplyDeleteThis really makes you think that maybe its possible to become a human calculator. At first i had thought that it was just a born talent that people had but the way that Alexis puts it, it seems to be more of a self taught skill.
http://www.dailymail.co.uk/sciencetech/article-501232/The-human-calculator-393-trillion-answers--picks-right-70-seconds.html
Willis Dysart ("Willie the Wizard") is a human calculator born in 1924. He quit school in third grade. He was hired by a radio station in 1940, during the presidential election, to calculate "the exact standing of any candidate on the board, including his current total, the percentage of votes counted at that point and the probable outcome of the contest on the basis of existing information" He did this much faster than the calculating machines other people were using. He would also show off by asking for the candidates' birthdays and calculating within seconds how many days they had been alive. His method for multiplication is grouping digits into groups of 3 before multiplying them, whereas most other human calculators do this in groups of 2.
ReplyDeleteThese human calculators make me feel somewhat worthless. I've become way too dependent on my calculator, and often find myself tempted to use it for things like 38/2. I SHOULD NOT NEED IT FOR THAT. So when I'm not taking a test, I try to always use mental math. It can be tough, though when it's 2 in the morning and all you want to do is go to bed. The last thing you want to do is mental math. Okay now I'm complaining.
But I was reading the other comments and I saw that Scott Flansburg seemed to think that it was a bad idea to teach people to add in the opposite direction we read. I don't really know what would be so bad about that, but it's interesting to me because I actually add "backwards" in my head; left to right. I add the digits on the left then move right, and if I have to carry a digit, I move back left, add it to the digit there, and continue right. I was taught to do it right to left, but I've never really done that because it feels unnatural. When I multiply, I do it the way demonstrated with the tiles, but without visualizing them (if I'm making any sense…), I do 40x40, then 2x3, then add them, then 2x40, then add that, then 3x40, then add that.
The thing about mental math is for me it's so fallible. THe problem is that when I start doing it on paper, I often get impatient because my mind starts getting ahead of my hand and then I end up just finishing in my head, anyway. This is the same for algebra problems. I think this is why I make a lot of the mistakes I make.
Everyone in period two knows that i cannot do any sort of calculation in my head. So what i do is i split up the numbers into smaller more manageable numbers. So for 42x43, i would split them up into small numbers that i can deal with. so first i would divide both numbers by 10. so i would end up with 4.2x4.3. by doing this you just made the number way smaller and more manage able. Then you multiply the two numbers together, and get 18.06. You then know the answer is 1806.
ReplyDeleteThis way is still not that great if you are someone like me who cant do any sort of math in there head. My advise is just write it out, or buy a calculator, because i get paranoid and don't think my answer is correct.
Math Jokes
ReplyDeleteQ: Why don't you do arithmetic in the jungle?
A: Because if you add 4+4 you get ate.
Q: What do you call friends who love math?
A: algebros
Q: What do you call a number that can't keep still?
A: A roamin' numeral.
Q: What does the zero say to the eight?
A: Nice belt!
Teacher: Did your parents help you with these homework problems?
Pupil: No I got them all wrong by myself !
Expand (a+b)^n.
Solution:
(a+b)^n
(a + b) ^ n
(a + b) ^ n
(a + b) ^ n
Q: Why isn't alcohol served at a mathematician's party?
A: Because you shouldn't drink and derive.
Q: What do you do to warm up if your room is cold?
A: Stand in the corner. It's 90 degrees.
Q: Have you heard the latest statistics joke?
A: Probably.
Come on Algebra, stop asking us to find your "x", she's not coming back and don't ask "y" either.