Mental math

Quote "how to multiply and 2 digit number by 11 "

Question: how did they find this out that it works? when did they start noticing a pattern in numbers with 11 and 12 and other large numbers?

comments: i found this really helpful because multiply large numbers has never been easy for me and i always have to write it out and do it the long way. the eleven one really is so easy i like this one a lot its a super easy pattern to remember and these little rules will help me to finish on timed test in college a lot faster when i dont have a calculator but what i really think is interesting is how people found out these work like who took the time to find these patterns.

Flow

Quote: " it is by being fully involved with every detail of our lives weather good or bad that we find happiness not by trying to look for it directly"

question: I have a hard time understanding the bad part in this quote because when i become fully involved with something bad that is happening in my like my mindset is very negative. i feel like it is smarter to be fully involved with the good so that the bad is almost non existent i wonder what is the happiness that can be found when you are fully involved with the bad?

comment: i agree when you are fully invested or involved with w/e you are doing you are much happier. i also agree that when we do something that is difficult and that really stretches out and works our minds we are much happier when we finish or complete w/e we are working on. I dont get any satisfaction when i do something that was really easy because it wasn't worth my time because it comes to easy.that is why people have to constantly challenge themselves and be competitive. when i finish the school week knowing that i had to work hard all week to finish everything that has to be done i am so happy when i have 2 days off. but when i dont really do anything all week the weekend is not as exciting.

Drive

Quote: "those who have an entity theory believe that intelligence is just an entity, it exists within us, in a finite supply that cannot increase. those who subscribe to an incremental theory take a different view. they believe that intelligence may very slightly from person to person it is ultimately something that with effort we can increase."

Questions/comment: i realize that we all have different views on what intelligent is, and if we can learn to mastery things but i wonder if are views change at different ages? for example when i was alittle kid i thought i could do anything because my parents told me i could if i put my mind to it. My mind was like a sponge i enjoyed learning i loved school everything was interesting and i always wanted to know more. Now that i have hit my teenage years my view on wanting to learn everything has changed sometimes i will see a math problem and think i cant do that. maybe this is my mind set and that is what is causing me to not excel in math? or is it my age? could it be that when you hit a certain age you begin to think in a entity theory way? i believe this would be an interesting study if you look at the theory's people believe in terms of age if you can find out something because i do believe it has something to do with age. at the same time i know from experience and from examples that you can achieve anything with a lot of hard work and the right mindset. this article reminds me of the book/ documentary "the secret."

50 life secrets and tips

quote: "the required about of sleep is for normal people..... you can be fine with 2 hours of sleep per day."

question: where did they get this information from? is it proven by doctors?

Comment: I honestly don't believe that you would be okay with only 2 hours of sleep a day that doesn't make any sense at all. your body needs time to rest. sleep is proven to be good for you so why would you want to drain your body and not recharge it the appropriate amount. it doesn't make sense to me. i chose this quote because its the only one i didn't agree with at all i really liked the reading but this part just sounded crazy to me. I also think that we should have more readings like this one because i found it really interesting.

project ideas

I think it would be really fun if we did videos on what calculus is to us. and people can apply what we learn by choosing a specific aspect of calculus that they like or hate or anything and we can make comedy's, action or any type of video to get our points across in a fun and interesting way.

This connects to the real world because we are taking the things we learned in the class room and turning it in to something that anyone can enjoy.

Another project we could do is make something we caculus im not sure what we could make but that would be fun.

ch 1

Quote: "despite being so special there are an awful lot of them."

Question: why do people find these numbers so special i must not understand the importance?

Comment: this article touch on some very interesting things. one being how special one is to everyone and i have to agree it is a very specail number. It was the first number that i learened how to understand. more Importantly it has helped to be the gate way to math for alot of people because once you understand one you can say one plus another one and then that can explain how you get to the next number two. I think these numbers are the easest for me to understand primes and natural numbers when it comes to the other articles i prefer reading about these because i can realate with these numbers and there easier to look at. i find it so interesting that a 16 year old boy discovered the pairs in math I wish i can find something in math like that. amicable numbers are supposable perfect but who desides what was perfect or not. i think these are some really interesting ideas brought up in this reading

ch0.000000001

Quote: we now know that much of the world is invisible to us because the human i can not see.

question: I feel like this is something that took people along time to grasp what was it that made people realize that decimals and small numbers were real when so many people believed there were only whole and rational numbers?

Comments:

i find it amazing that we have found smaller numbers that have lead us to the world of science more like with out this math we would not have been able to do alot of the things we do today. i always have been so interested in science and have never really cared for math but this makes me have a deeper appreciation for all the people that have spent there life trying to find the information that i talk for granted of a daily bases. math opens up a knew world it helps you to see things that you may never see but you can understand. and with out this information you know nothing truly about the world around you. another thing that i found interesting about this article is that they used counting boards to find out information. that seems like alot of work and how in are time we are so lazy its hard for us to even pull out a calculator its really crazy.

i still cant see how they could understand this in there time because i dont know how i could grasp all this information when you think about math and small numbers it makes me feel like things are less clear instead of more clear

ch 0

Quote: some people ask weather a hand-clap in a forest that nobody will actually sound. of course it does sound does not require ears, it is a vibration of molecules. similarly a number or a pattern that is seen by no one is still a number, weather we are there or not.

Question: I realize that sound has vibration but I dont understand how they bring the numbers in to this?

Comment: i like how it says a number is a number weather we see it or not i think that is really interesting because i constantly find myself saying you cant get a number from this or that. this helped me realize that just because i don't see a number now or a pattern maybe another animal can. It also makes me think we have so much time to find out new numbers about the world like we always are finding knew ways to solve things or math we didn't understand before. Its really interesting to think that math needs us and we need math. This reading helped me have a better understanding of math and why we do it. It makes me think its more important then i thought before i read this. You always hear people say math is important but this puts it more into perspective and reality to me.

Gauss

Quote:" you know that I write slowly. this is chiefly because i am never satisfied until i have said as much as possible in a few words , and writing briefly takes far more time than writing at length."

question: how does writing briefly take far more time?

thoughts: I find it weird that he is not satisfied if he doesnt say things in a few words. it doesnt really make that much sense to me. if you need to write more to fulling express yourself you should. I also dont see what the problem with being lengthy with your writing if it might be clearer and easier to do. It almost seems like he trys to make things harder on him self. he also mad it so hard for others to understand and learn the things he had found.
i honestly think he might be alittle selfish." he is like a fox" what exactly do they mean by this is this a bad thing. i think it might be because he finds things and trys to hide them from every one. you can tell he is very different from the last guy we read about because the other guy was clear in his writing and he made sense and it seemed he wanted people to learn and he made it easy for them so i like him better then this guy. i dont see how someone so smart would want others to learn maybe he thought he was so much smarter then everyone else and they would never understand what he was saying thats the only reason why i could see him saying it was " useless to teach" i'm not sure i like this guy. I think its great he was really smart but i dont like his reasoning's.

QQC

"his writings are models of relaxed clarity."

i really like the way this sentence was written it explains how well he could put his thoughts in to words. it is almost like he is a really graceful writer. i always thought math brains were only good at math but he obviously could explain him self through text which is simply beautiful. It makes me think of him as a peaceful man who's mind is very clear as if there is no confusion although this is a great thing to say about him i have a few questions.

question: relaxed clarity can mean alot of things what does it mean in context? also most mathematics geniuses have some type of mental illness did he?

"he calculated without apparent effort, as men breathe, or as eagles sustained themselves in the wind."

when i saw this all i could think is wow i wish i was him if i could calculate like i breathe i would not be stressing over math class..haha. i constantly wonder how some people are naturally good at math. teachers always say it is practice and everyone can be really good at math even though i agree to a point i still think there are people that are born and just good at math and they can pick it up super quick and some people that just don't have the ability.

Question: How is it that he can do this i thought it was something you must learn to do maybe its something you are born with?