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Practice mental Day of the week calculation


Practice Mental Day of the week Calculation: vs. 1.1
 
Press the Button to get the next test date
Century Options:
1700
1800
1900
2000
Select one or more centuries for expanding range of test date
    Answer:
Select the correct weekday from the drop downlist
 
    Score:

 
 
Press the Clear Button to erase the Result
    
Press the Print Button to print the Result
    
 
  • Result
  • Help

Practice Mental calculation of cubic root in your head

Click the get next test number button to randomly generate a 1, 2 or 3 digit cubic number so you can practice calculated the cubic root of that number.

Email me if you encounter any problems at hve@hvks.com

There is an excellent website for mentally calculating 1-2 digit square root at http://mindmagician.org/sqrt.aspx and for 1-2 digit cubic root at http://mindmagician.org/cubert.aspx
Another webiste for mentally calculating cubic root for 3 digits number can be found on http://thinkinghard.com/blog/CubeRoots.html
All theses web sites describe the method in details, so no need to bring it here.

 


Mental calculation of the week day of the week for any dates

Using the technic describe below can be used as a good party trick or just a way to stimulate and keep your brain sharp. On the internet you can find several methods describe different way of achieving the same answer for the day of the week. I personally find below methods the easiest way of doing it and the fastest to learn. I first came across this method via Arthur Benjamin (https://www.math.hmc.edu/~benjamin/ ) who is the wizard of mental math calculation and can be found on Youtube or ?The secrets of Mental Math? on www.TheGreattCourses.com The only math you need to know is to be quick in adding 1 or 2 digits number together, memorize months and century offset and also be quick in taking a number modulus 7. (calculating the remainder of dividing by 7, for shorthand we will use the C language operator for modulus %).
The technic is simple and straightforward for a given day in the format DD/MM/YYYY.
Start with the year (YYYY) and for simplicity we split up the year in a 2-digit century and 2-digit year within the century. E.g. CCYY.

  1. We start with the YY and do nothing other that remember the year. This is known to be the year offset. YY
  2. Next, we find how many leap years we have experience so far in this century by dividing the year with 4 and take the whole number the year divide up in 4 and add it to the number from step 1. ?E.g. For year 58 you get 58/4=14
  3. Next you add the century offset to number. Here you must memorize a few number. For the 19th hundred it is 0, for the 18th century it is 2, for the 17th century it is 4 and for the 16th century it is 6 and then the number sequence repeat itself both up and down.
  4. Century

    16th

    17th

    18th

    19th

    20th

    21th

    22th

    23th

    Offset

    6

    4

    2

    0

    6

    4

    2

    0

  5. Next step is to add the Months offset and here we need to memorize a few more numbers.
  6. Months

    Jan

    Feb

    Mar

    Apr

    May

    Jun

    Jul

    Aug

    Sep

    Oct

    Nov

    Dec

    Offset

    1

    4

    4

    0

    2

    5

    0

    3

    6

    1

    4

    6

    Remember

    122

    52

    62

    122+

    Arthur Benjamin cleverly suggested for each quarter, 12 square, 5 square, 6 square and a little bit more than 12 square to remember the offset and it actually works out great. Easy to remember and easy to calculate. E.g. The months of September has an offset of 6 while month of April has an offset of 0.

  7. Next step is to add a possible leap year offset only valid for the first wo months (Jan and Feb). The offset is a fix constant of -1 otherwise 0 if the months are from Mar-Dec
  8. Lastly, we add the day of the months DD to our result.
  9. We take all the offset we have added from step 1 to step 6 and find the remainder after dividing it by 7. The result is a number between 0 and 6 and the day of the week is as follows.
  10. Result modulus 7

    Day of the Week

    0

    Saturday

    1

    Sunday

    2

    Monday

    3

    Tuesday

    4

    Wednesday

    5

    Thursday

    6

    Friday

Lets see how it works on a real example of lets say September 4, 1957, 22 February 2004 and of course Albert Einstein birthday 14 March 1879?

Date

Offset

04/09/1957

22/02/2004

14/03/1879

 

YY

Year offset YY

57

4

79

Number of leap year (YY/4)

14

1

19

CC

Century offset (CC)

0

6

2

MM

Months offset (MM)

6

4

4

Leap year month offset

0

-1

0

DD

Day in Months (DD)

4

22

14

 

Total

81

36

118

 

Result modules 7 (%)

4=Wednesday

1=Sunday

6=Friday

As always you need to practice mastering the mental calculations and the practice calculator above will help you quickly obtain your skills to do it fast and accurately. There are some short cuts you can apply along the way. E.g. you don?t need to wait until all the digits has been calculated and added together to do you modules 7 calculation. You can do it along where it makes sense. E.g. Albert Einstein?s birthday 14/03/1879. Notice that after the first 2 offsets the result is 0 meaning we can forget the YY and number of leap year calculation to free up your brain to do the remaining calculation. I usually apply this short cut only to the first two offsets calculated to reduce the accumulated number. The accumulated of the other offsets will be less than 43. Making it faster to do the modulus 7 calculation of the total sum at the end.


Offset

14/03/1879

Accumulator

Year offset YY

79

79%7=2

Number of leap year (YY/4)

19

(2+19)%7=0

Century offset (CC)

2

2%7=2

Months offset (MM)

4

(2+4)%7=6

Leap year month offset

0

(6+0)%7=6

Day in Months (DD)

14

(6+14)%7=6

Total

118

6

Result modules 7

6=Friday

6=Friday

Have fun


Corrections:
28-Dec-2017 Vs 1.1 Improve description of method used and minor bugs
21-Jun-2017 Vs 1.0 Initial release of practice mental day of the week calculation
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