Math & Magic
Magic is considered an art form because art is simply a way of self-expression. Although it is obvious that a deck of cards may not be art, similarly to how a paintbrush is not art, when placed in the hands of the right person, art is created.
At first glance it may seem as though mathematics and magic could be near polar opposites. These two things seem to have nothing in common but in fact, upon close investigation many connections and similarities between math and magic reveal themselves
Many powerful magic tricks and magical effects have a mathematical basis. Let us explore one example.
The Fast Five Trick:
This trick involves impressing people with your ability to divide any number by 5 at super speed, no matter how large the number, and do the calculation correct to one decimal point.
Dividing a large number by 5 can actually be done by a very simple 2-step method.
Step 1: multiply the number by 2
Step 2: move the decimal point
The math
Easy example: Say 10 (divided by 5)
Step 1: 10 X 2 = 20
Step 2: Shift the decimal point, so 20 now becomes 2.0 or 2
Harder example: Say 190 (divided by 5)
Step 1: 190 X 2 = 380
Step2: Move the decimal point, so 380 becomes 38.0 or just 38
Even harder: Say 4567 (divided by 5), seems tough without a calculator!
Step 1: 4567 X 2 = 9134
Step 2: Move the decimal point, so 4567 becomes 913.4
Even HARDER: Say 123456789 (divided by 5)
Step 1: 123456789 X 2 = 246913578
Step 2: Move the decimal point and the answer is 24691357.8
Lets explore the math behind this trick:
Dividing by 5 is the same thing as doing half of a divide by 10. Dividing by 10 is easy because you simply move the decimal (a 100 divided by 10 is 10.0, 56 divided by 10 is 5.6 and so on). Division can also be written as fraction (100÷10 is 100/10, 56÷10 is 56/10 and so on). If you do the same thing to the numerator of a fraction as you do to the denominator the ratio remains the same (6/2 = 3/1 =12/4 = 3). Therefore taking any number A and dividing it by 5 means that A/5 = (2XA)/10. Mathematicians come up with algorithms and then show mathematically that it will always do what it is supposed do, which is exactly how this magic trick was created!
References
The Manual of Mathematical Magic by Peter McOwan and Matt Parker
McOwan, P., & Parker, M. (n.d.). The manual of mathematical magic. Retrieved from http://www.mathematicalmagic.com/docs/mathsmagic_full.pdf
The Fast Five Trick:
This trick involves impressing people with your ability to divide any number by 5 at super speed, no matter how large the number, and do the calculation correct to one decimal point.
Dividing a large number by 5 can actually be done by a very simple 2-step method.
Step 1: multiply the number by 2
Step 2: move the decimal point
The math
Easy example: Say 10 (divided by 5)
Step 1: 10 X 2 = 20
Step 2: Shift the decimal point, so 20 now becomes 2.0 or 2
Harder example: Say 190 (divided by 5)
Step 1: 190 X 2 = 380
Step2: Move the decimal point, so 380 becomes 38.0 or just 38
Even harder: Say 4567 (divided by 5), seems tough without a calculator!
Step 1: 4567 X 2 = 9134
Step 2: Move the decimal point, so 4567 becomes 913.4
Even HARDER: Say 123456789 (divided by 5)
Step 1: 123456789 X 2 = 246913578
Step 2: Move the decimal point and the answer is 24691357.8
Lets explore the math behind this trick:
Dividing by 5 is the same thing as doing half of a divide by 10. Dividing by 10 is easy because you simply move the decimal (a 100 divided by 10 is 10.0, 56 divided by 10 is 5.6 and so on). Division can also be written as fraction (100÷10 is 100/10, 56÷10 is 56/10 and so on). If you do the same thing to the numerator of a fraction as you do to the denominator the ratio remains the same (6/2 = 3/1 =12/4 = 3). Therefore taking any number A and dividing it by 5 means that A/5 = (2XA)/10. Mathematicians come up with algorithms and then show mathematically that it will always do what it is supposed do, which is exactly how this magic trick was created!
References
The Manual of Mathematical Magic by Peter McOwan and Matt Parker
McOwan, P., & Parker, M. (n.d.). The manual of mathematical magic. Retrieved from http://www.mathematicalmagic.com/docs/mathsmagic_full.pdf