Question
What are the best math tips? Are there any shortcuts or alternative methods for remembering formulas that can help with mathematical challenges in daily life?
Answer
There's an entire book of math hacks invented by a concentration camp survivor, the Trachtenberg System.
http://en.wikipedia.org/wiki/Tra...
A simple hack, the first one I learned, is that you can generate the 9-times multiplication table by simply writing down the digits 0-9 down a column and then up a column, like so.
09
18
27
36
45
54
63
72
81
90
The divide-into-72 hack for compound interest mentioned by L (Luis) Figueroa is also great, especially because people suck at compound interest thinking.
Another simple hack is useful when multiplying high place value numbers. If you are doing 99x3, it is easier to do 100x3 -3 than to do the direct computation. This particular trick helped me win a point in a math quiz in grade school :)
Another interesting one is Celsius to Farheneit conversions. The correct transform is F = 9/5C +32, but F = 2C+30 is a great approximation.
I really love approximations. Most people don't really stop think about the accuracy and precision required in an answer for a specific purpose. "Roughly right" is a great design principle to follow in all decision-making, and math approximations are central to that kind of thinking.
22/7 is a hack for the value of pi (3.14281428.... instead of 3.1415926....)
Memorization is probably one of the other best general underlying math principles for generating math hacks. The Rule of 72 is one example. There are plenty of other such useful memorization hacks. For example, in control theory, it is useful to remember that in a step response, a dynamic system will reach about 63% of its terminal value in one time constant. With statistics, it is useful to remember that a standard deviation contains about 68% of the mass of a distribution. 3-sigma gets you to 99.7%, 6-sigma gets you to less than one in a million defects in a spread.
There are also plenty of qualitative hacks to remember in analyzing graphs and data. For example:
In fact, I'd venture to say that practical mathematics is nearly all about having fun with hacks.
http://en.wikipedia.org/wiki/Tra...
A simple hack, the first one I learned, is that you can generate the 9-times multiplication table by simply writing down the digits 0-9 down a column and then up a column, like so.
09
18
27
36
45
54
63
72
81
90
The divide-into-72 hack for compound interest mentioned by L (Luis) Figueroa is also great, especially because people suck at compound interest thinking.
Another simple hack is useful when multiplying high place value numbers. If you are doing 99x3, it is easier to do 100x3 -3 than to do the direct computation. This particular trick helped me win a point in a math quiz in grade school :)
Another interesting one is Celsius to Farheneit conversions. The correct transform is F = 9/5C +32, but F = 2C+30 is a great approximation.
I really love approximations. Most people don't really stop think about the accuracy and precision required in an answer for a specific purpose. "Roughly right" is a great design principle to follow in all decision-making, and math approximations are central to that kind of thinking.
22/7 is a hack for the value of pi (3.14281428.... instead of 3.1415926....)
Memorization is probably one of the other best general underlying math principles for generating math hacks. The Rule of 72 is one example. There are plenty of other such useful memorization hacks. For example, in control theory, it is useful to remember that in a step response, a dynamic system will reach about 63% of its terminal value in one time constant. With statistics, it is useful to remember that a standard deviation contains about 68% of the mass of a distribution. 3-sigma gets you to 99.7%, 6-sigma gets you to less than one in a million defects in a spread.
There are also plenty of qualitative hacks to remember in analyzing graphs and data. For example:
- An exponential will eventually overtake a polynomial
- Half the growth in a doubling process will be in the last step
- Circles cannot be squared, angles cannot be trisected (basic Euclidean geometry facts)... saves pointless effort
- Everything becomes easier if you can transform stuff to matrix-and-vector formats
In fact, I'd venture to say that practical mathematics is nearly all about having fun with hacks.