Math Projects for Science Fairs

1. Investigate ``big'' numbers. What is a big number? The following examples might guide your investigation. A bank is robbed of 1 million loonies. How long would it take to move them? How much would they weigh? How much space would they take up? How big a swimming pool do you need to contain all the blood in the world? Is tex2html_wrap_inline264 very big? What is the biggest number anyone has ever written down (check the Guiness book of world records over the last few years)? How did this number come about?
2. How do computer bar codes (the ones you see on everything you buy) work? This is an example of coding theory at work. Find others. Investigate coding theory - there are many books with titles like ``an introduction to coding theory'' (this is not about secret codes). References: [Gal1], [Gal2], and [Gal3].
3. Infinity comes in different ``sizes''. What does this mean? How can it be explained? References: [Kam] or [Hunt] or refer to any book on Set Theory.
4. It is easy to check if a number is divisible by 10 by looking to see if its last digit is a 0. Haw many other ``tests of divisibility'' can you find? Divisibility by 5 or 7 or 9? Why do they work? Reference: [Gard1].
5. Most computers these days can handle sound one way or another. They store the sound as a sequence of numbers. Lots of numbers. 40,000 per second, say. What happens when you play around with those numbers? eg. Add 10 to each number. Multiply each number by 10. Divide by 10. Take absolute values. Take one sound, and add it to another sound (i.e. add up corresponding pairs of numbers in the sequences). Multiply them. Divide them. Take one sound, and add it to shifted copies of itself. Shuffle the numbers in the sequence. Turn them around backwards. Throw out every third number. Take the sine of the numbers. Square them. For each mathematical operation, you can play the resulting sound on the computers speakers, and hear what change has occurred. A little bit of programming, and you can get some very bizarre effects. Then try to make sense of this from some sort of theory of signal processing. You will first have to discover how sound is stored.
6. Find out all you can about the Fibonacci Numbers, tex2html_wrap_inline276 . In particular, where do they arise in nature? For example, look at the spirals on a pine-cone -- following the pattern of the cone, one spiral will go left, the other right. The cone will be covered by ``parallelograms'', the number of seeds on each side of the parallelogram will (always?) be two neighbouring Fibonacci numbers. For example 5 and 8. Similarly for pineapples, petals and leaves on plants.
7. What is the Golden Mean? Study its appearance in art, architecture, biology, and geometry, and its connection with continued fractions, Fibonacci numbers. What else can you find out?
8. Find out all you can about the Catalan Numbers, 1, 1, 2, 5, 14, 42, ...
9. Investigate triangular numbers. If that's not enough, do squares, pentagonal numbers, hexagonal numbers, etc. Venture into the third and even the fourth dimensions. Reference: [C&G].
10. Build models to illustrate asymptotic results such as Stirling's formula or the prime number theorem.
11. There is a well-known device for illustrating the binomial distribution. Marbles are dropped through the top and encounter a number of pins before dropping into cells where they are distributed according to the binomial distribution. By changing the position of the pins one should be able to get other kinds of distributions (bimodal, skewed, approximately rectangular, etc.) Explore.
12. Investigate the history of pi and the many ways in which it can be approximated. Calculate new digits of Pi - see the web site [Pi] to discover what this means.
13. Use Monte Carlo methods to find areas or to estimate pi. (Rather than using random numbers, throw a bunch of small objects onto the required area and count the numbers of objects inside the area as a fraction of the total in the rectangular frame).
14. Explore Egyptian fractions. In particular consider the conjectures of Erdös and Sierpinski: Every fraction of the form tex2html_wrap_inline278 or tex2html_wrap_inline280 , tex2html_wrap_inline282 can be written in the form tex2html_wrap_inline284 , where a < b < c, and a, b, and c are positive integers. See what you can discover. References: [Stew], [S&R].
15. Look at the ways different bases are used in our culture and how they have been used in other cultures. Collect examples: time, date etc. Look at how other cultures have written their number systems. Demonstrate how to add using the Mayan base 20, maybe compare to trying to add with Roman numerals (is it even possible?) Explore the history and use of the Abacus. References: [Bak], [Ifr].
16. There are several methods of counting and calculating using your fingers and hands. Some of these methods are still in common usage. Explore the mathematics behind one of them. Reference: [Ifr].


Source: Canadian Mathematical Society
Topics: Science Fair Project Ideas

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Masuk kedalam kuadran manakah Anda ?

enurut Robert T. Kiyosaki dalam buku the Cashflow Quadrant, berbagai macam cara orang mendapatkan uang atau mendapat nafkah hidupnya dapat digolongkan kedalam 4 kuadran, yaitu :

1. Employee : Karyawan atau buruh;
2. Self Employee : Dokter, Pengacara, Artis, Pelawak;
3. Business Owner : Pemilik Toko, Pemilik Kontrakan, Pemilik rental mobil;
4. Investor : Penanam modal atau investor.

Nah, melihat contoh tersebut diatas, masuk kedalam kuadaran manakah Anda sekarang? Sebab bisa jadi pola pikir kebanyakan bangsa kita hanya sebatas Employee?

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Building Family Strengths: Values

Values are a reflection of who we are, of our culture and of our own unique heritage. Being clear about our values enables and empowers us to establish priorities and make decisions that we can live with and by. What we learn from our families in childhood builds character and serves us throughout our lives. Families guide personal growth and education, while offering love and protection. When families are strong, our neighborhood is strong, our nation is strong and we can be more hopeful about the future.

Values have influence at every stage of making a choice. Values shape what we believe and perceive. They influence our goals, the alternatives we select and the ranking of these alternatives.
What Are Values?

Values are a part of our experience that affects our behavior. They encompass our attitudes, the standards for our actions and our beliefs. Values are often learned from family, culture and people around us. In addition, values tell others what is important to us and guide our decision making. We use our resources - time, money and brain power - on the things we value.
Characteristics of Positive Values Within Families

Many of our family ideals, beliefs, behaviors or "values" are merely habits of thinking or behaving. Sometimes this is because we do not know any other way or because we have not stopped to think about the motives or reasons for the things we think, say or do. Identifying and communicating the values of the family can . . .

* Be helpful in making personal decisions.
* Become a guide for self-empowerment.
* Help manage time, energy and resources to the fullest.
* Help one to know oneself better.
* Help eliminate some of the confusions in life.
* Help formulate a desired system of values.
* Help one to act or behave in accordance with their values.
* Help one to better understand and respect others who have different values.

Values are critical in building character and increasing an overall sense of well-being. Positive values within families...

* Promote honesty, integrity, commitment and loyalty.
* Encourage respect for self and others and tolerance of differences.
* Require being responsible and accountable for your actions, while practicing selfcontrol.
* Teach fairness and treating people equally.
* Require consideration, kindness, compassion and generosity toward others.
* Foster being a good citizen who appreciates doing things which make life better for self and for other people.

Preschool Children

Younger children are concerned with being good people. Being good means seeing the difference between right and wrong - and then doing what's right! Being good is about being brave. It's about doing what's right when it costs more in friends, money, toys or treats than we want to pay. Doing the right thing consistently is hard for anyone - but especially this age group.
Elementary Children

Young children need to know how to act and how not to act. They need to have clear instructions - not conflicting messages from family members and others in their lives. Through the many interactions between school-age children and others around them, the child learns what is acceptable, and what is not. Much of what this age group values will be played out at school, on the playground and through other interactions with their peers.


by Brenda J. Thames, Ed.D., CPCS, Extension Program Development Specialist|Deborah J. Thomason, Ed.D., Extension Family & Youth Development Specialist
Source: Clemson University Public Service Publishing
Topics: Parenting and Families, Parenting

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Understanding Your Child's Temperament

Since temperament is an inherent part of your child’s character and can be shaped but not changed, it is important that you remain flexible as a parent and sensitive your child’s needs. Understanding and learning more about your child’s temperament is important because it affects your child, you as a parent, and the relationship between the two of you.
Understanding your child’s temperament will help you:

* Explain which behaviors are typical for your child
* Anticipate how a child will react to a particular event or situation
* Interact with your child
* Know which types of discipline will be effective
* Be more confident in yourself as a parent
* Create a positive relationship between you and your child

Misunderstanding your child’s temperament can lead to:

* Criticizing or punishing your child for behavior that is an expression of your child’s temperament
* Parenting your child in a way that works against your child’s temperament, which can lead to behavioral problems
* Blaming yourself for being an ineffective parent

Creating a good fit

The better the fit between the child’s temperament and the parenting style, the better the results will be. Many parents with more than one child are often surprised at how different siblings can be. In many cases, what parenting style worked for the first child will not work with the second, and parents will have to use completely different techniques in raising each child. Treating children differently does not mean that you are treating them unequally or unfairly—one child may need more structure and guidance while another may do better following an independent path. It is also important for parents not to let their hopes of what their child will be like take too much precedence over what the child actually is like. Behavioral problems result when the parenting style and the child’s temperament do not make for a good fit.

Creating a good fit does not mean that you let your child do anything she wants, or behave in any way she wants. Rather, it means that you can understand her actions and behaviors better and respond appropriately. Learning about temperament will help you find a discipline technique that is both positive and effective, and it will help you decide on which issues you need to remain firm and which ones you can let slide. Taking these characteristics into consideration, you can learn how to help your child rather than becoming frustrated and critical when your child acts in a way you do not understand.

* Perhaps your child always cries when you try to dress her up in fancy dresses or bundle her up for the cold. She may be upset because she is highly sensitive, and the scratchiness of the clothing is uncomfortable.

* If your child is bouncing off the walls at home and refuses to calm down—even at meal times and bed time--perhaps you should enroll her in a gymnastics class or sign her up for a children’s softball or soccer league. Do not expect your active child to be able to sit still for long periods of time—this will be next to impossible for her to do. Therefore, break up long car rides and quiet activities with games and physical activity. If her energy level is channeled in a positive way, it will help her keep out of trouble.

* A child who always cries before going to school may be having difficulty adjusting, or may be quite shy. Help your child get used to people in a slow and controlled manner, and talk to your child about her feelings.

Source: Center for Child Well Being
Topics: Temperament and Personality, more...

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Ternyata Ayam Lebih pandai Membedakan Warna

Para peneliti di Washington University School of Medicine di St. Louis, USA baru saja melaporkan penemuan mereka tentang disain biologis luar biasa yang ada di mata seekor ayam. Ternyata, seekor ayam memiliki lima jenis reseptor cahaya di matanya. Hebatnya, kelima reseptor tersebut terjalin sedemikian rapinya sehingga kesemuanya ada di seluruh bagian retina, sementara reseptor yang sejenis tidak ada yang saling bersebelahan. Subhanallah, puji Tuhan! Jalinan kelima reseptor yang demikian rapinya membuat seekor ayam dapat melihat banyak sekali warna di bagian manapun di retinanya.

Menurut Joseph C. Corbo, MD, PhD, seorang penulis senior yang merupakan seorang asisten profesor dalam bidang patologi dan imunologi serta dalam bidang genetik, pengaturan reseptor warna yang sedemikian rapinya sangat jauh melampaui apa yang terdapat di retina mamalia, termasuk manusia. Akibatnya, ayam lebih baik dalam membedakan warna ketimbang manusia! (Wah, untung ayam tak dapat membuat test buta warna, bisa jadi kita tak lolos test yang mereka buat lho - red)

Retina manusia memiliki reseptor yang sensitif terhadap panjang gelombang untuk warna merah, hijau, dan biru (RGB - Red, Green & Blue). Sementara retina ayam (atau unggas), selain memiliki reseptor untuk panjang gelombang ketiga warna tersebut, juga memiliki reseptor yang dapat mendeteksi panjang gelombang untuk warna ungu (violet) - termasuk ultraviolet - dan sebuah reseptor ganda yang diyakini oleh para peneliti membantu unggas untuk mendeteksi gerakan.

Susunan kelima reseptor yang tersebar merata di seluruh retina dan tak adanya reseptor sejenis yang saling bersebelahan memberi petunjuk adanya aturan yang berlaku menyeluruh, bahwa setiap reseptor dapat saling berdekatan, kecuali dengan reseptor sejenis. Dan ini dapat membantu para peneliti mempelajari kemampuan penglihatan manusia. Prof. Corbo pun menyatakan bahwa mereka berencana untuk mengembangkan penelitiannya ini untuk dapat dikaitkan dengan pemanfaatan stem cell dan teknik lain agar mampu menyembuhkan hampir 200 jenis kelainan genetik yang menyebabkan kebutaan. Semoga di kemudian hari saudara-saudara kita yang terkena gangguan penglihatan dapat menikmati hasil penelitian ini dan mampu melihat gemerlapnya dunia dengan terang benderang!

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