An Explanation Why the Line Multiplication Trick Works

Mathematical concepts and operations can be represented in different ways. For example, a function can be represented using a table, set of ordered pairs, equations, or graphs. Another example is an equation which can also be represented as a balance.

In this post, we are going to discuss a representation of a simple concept which is very popular among netizens: multiplication of numbers using lines. Many are amazed about this representation that they even call it the magic line multiplication trick.

Note: If you don’t know the trick, watch first the video below. 

Now, let us learn why the line multiplication trick works.  Continue reading

Who is the greatest mathematician?

For you who is the greatest mathematician? This was a question asked to me by a kin, a freshman who is currently studying a  mathematics related course. This question is probably asked by many others who are just starting studying mathematics or those who are just simply curious.

Asking who the greatest mathematician is like asking who the greatest singer is. Singers have different genre that it is nearly impossible to tell. Pop lovers would probably suggest that it was Michael Jackson, but classical singers would probably disagree and would suggest some names like Luciano Pavarotti.

I think, determining the greatest mathematician is even more complicated than determining the greatest singer. Mathematicians lived in different times and the maturity of mathematics at different times is enormously different. For example, during the time of Euclid, it takes a high-caliber mathematician to prove that the inscribed triangle in a circle containing its diameter is right, while they can be easily proved by eighth graders of the present time. Of course, we cannot claim that our eighth graders are better than or even at the same level as Euclid because mathematics has changed so much.  Those who are only read by mathematicians during the time of Euclid are now taught in the elementary and high school levels.  In addition, mathematicians study different fields and it is impossible to compare the level of difficulty or even to quantify the effect of their contributions. Continue reading

What If We Have 12 Fingers?

Our number system is called the decimal system (deci means 10) because we count in groups of 10’s. This is probably because we have 10 fingers. What do I mean when I said when we count in groups of 10?

The Human Fingers

Our number system has the digits 0 to 9, and then we when we reach the 10th number, we place 1 in the tens place 0 in the ones digit. In the decimal number system, 23 means that we have 2 tens and 3 ones. Similarly, the number 452 means that we have 4 groups hundreds (10 tens), 5 groups of tens and 8 ones. In fact,  if we use the expanded notation, 452 is equal to

4 \times 10^2 + 5 \times 10^1 + 2 \times 10^0.

Notice that each number is multiplied by powers of 10. Continue reading

Googol and Google

In last week’s post, we have talked about large numbers and their importance to scientific studies and everyday life. In this post, we talk about one of the most famous large numbers: googol.

A googol is the name of the number which is 10^{100} or a 1 followed by one hundred zeros. If you are wondering how large it is, well it is fairly large since the number of atoms in the observable universe is only 10^{80}. That means that we need 10^{20} universes, the size of the observable universe, to create a universe with googol number of atoms.

googol

The term googol was coined in 1938 by Milton Sirrota (he was 9 years old the time he invented the term), nephew of Edward Kasner, an American mathematician. Kasner was famous for his book Mathematics and the Imagination where he introduced the term googol. Continue reading

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