SNIPPETS  OF  MATH 


1. If you were born in the 20th century: 1901-1999
 Add the last two digits of the year you were born & your age:
the result will equal 112 in 2012 , 113 in 2013, etc.

2012-1939=7339+73=112

2013-1939=7439+74=113
 
If you were born in the 21stt Century: 2000 -2099
Add the last two digits of the year you were born & your age
the result will equal the last two digits of the current year

2012-2000=12 00+12=12

2013-2000=1300+13=13


2. Your task is to calculate the area of a circle:
multiply the diameter times its self, multiply by 22 and divide by 7
Circle with a diameter of 5 inches, determine the area.

5x5=25x22=550/7=78.57 sq. in.

Hint : 22/7=3.142=PI


3. Your task is to determine the diameter of a tree:
given the circumference.  
circum=88"; 88x7/22= diam

Hint: 7/22 is recipical of PI


4. Your task is to multiply any number of two figures by 11:

Rule: add the two numbers & place their sum between them.
43x11;      4+3=7         Thus: 473

Hint: if sum is greater than 10, add 1 to first number

65x11;      6+5=11       Thus: 715  


5. You task is to multiply any number of two figures by 12:

Hint: multiply by 11 & add the two numbers to the product

 45 x 11;     4+5=9    and: 495   Thus:  495+45=540


 72 x 11;     7+2= 9   and: 792    Thus: 792+72=864

96 x 11;      9+6=105   and: 1056    Thus: 1056+96=1152


6.  Your task is to extract the square root of any number:
Use a modern calculator!  
No, once the principle of squares is understood, it is a rather simple process and can be accomplished by simple multiplication and division.  

Hint: Divide the number into groups of two, beginning from the right  (the last group to the left can have either one or two digits).


 Example:
1225 = 12 25 - Hint: (12 is the ten’s group, 25 is the units group)

Solution - First step, find the number which will be in the ten's position - (12), 3 is the greatest square of 12, (3x3=9), therefore 3 is the ten’s number of the root. Remainder is 12-9=3.

Second step, find the number which will be in the units position.

 3X3=9; 12-9=3, +25=32; twice the tens number is 6; (2X3)=6; 6 will go into 32, 5 times. Therefore 5 is the units figure of the root.

12(10's group)   25(units group)
 ten's group: (3X3=9) therefore 3 is the 10's number of the square root   
unit's group: (2X3=6) and 6 will divide into 32 , 5 times, therefore 5 is the units figure
solution: 35x35=1225

Find the square root of 1890481?Answer: (2809)


7. Peculiar properties of the number 37.

When multiplied by each of the numbers in the progression 3, 6, 9, 12,15, 18, 21, 24,

will produce a result which is composed of 3 repetitions of sequentially increasing numbers; These numbers when added together will equal  the number used to multiply.

37        37            37                 37             37             37                37              37

 3           6              9                  12             15             18                21              24

111       222            333             444            555            666            777            888
 
1+1+1=3                   2+2+2=6                 3+3+3=9                4+4+4= 12

5+5+5=15                 6+6+6+=18             7+7+7=21              8+8+8=24


8. This is a mathematical process to illustrate predictable results of the base ten number system.

Step1. Choose any number between 1 & 9
Step 2. Multiply that number by 3
Step 3. add 3 to that result
Step 4. Multiply that number by 3
Step 5. Total will be a two (2) digit number\
Step 6. Add the two digits together

Result: The result will always equal 9


9. Another illustration of the predictable base ten number system.

Step 1. Pick any 3 numbers, none being zero
Step 2. Reverse the order of the chosen numbers
Step 3. Subtract the two groups of numbers
Step 4. The result will be another 3 number series,
Step 5. Add the last two groups.

Result: The result will be a four digit number whose value will always equal 1089


Mental Arithmetic

To add money, we reduce all currency to a decimal of the dollar and add.

50 cents = 0.50 of a dollar
25 cents = 0.25 of a dollar
10 cents = 0.10 of a dollar
Added, this combination equals 0.85 cents or 85/100th of a dollar; we process money without much thought.

The human mind can be trained to mentally apply this process to  a group of numbers. When performing mental arithmetic, convert the numbers being considered into groups no greater than 10. Using this proc stem helps to keep this effort simple.  The need to process numbers greater than ten (10) is not necessary. 

Now, let us apply this process to a mental procedure. Lets start with addition. We can add a long column of numbers using a method called ”Casting out Tens”. Our task is to add this group of numbers.

85+ 53+ 46+ 72+ 64+ 97+ 48  (first, arrange the numbers into a vertical column)

RULE: Begin at the top, on the units (right) side of the digits, cast out the tens and make a dot or dash each time a ten is dropped, add the excess (amount over 10) to the remaining numbers. Write the last excess (at the foot of the column) in the answer. Looking back, count the dots or dashes and proceed as before. The number of dots or dashes in the last column will give the left hand figure in the answer.  

(HINT: When, the bottom of the column, is an even ten,  make a dot and write a zero in the answer for that column. Should the number of dots in any column be 10 or more, place a dot at the top of the next column and add the excess to the same).

EXAMPLE:

Beginning at the top, units column (or the right side), added 5, 3 and 6 are 14; make a dash for the ten, add the excess 4 to the remaining figures, thus, 4, 2 & 4 are 10: make another dash and proceed, 7 & 8 are 15; make a dash for the ten and write the 5 in the answer. Carry the dashes or tens to the next column, saying 3 & 8 are 11, make a dash and add the 1 to the figures below and proceed the same as the first column. The bottom middle number is 6; there are  4 dashes in the last column, therefore 465 is the answer.  

  8- 5
  5  3
  4- 6-
  7  2
  6- 4-
  9- 7
  4  8-
46  5




                                                                  
                        Tidbits of Information

Longitude and Time

The circumference of the earth is divided into 360 degrees. Consequently the sun apparently passes over 360 degrees in 24 hours or 15 degrees per hour, or 1 degree in 4 minutes- hence these simple rules.

Multiplying the longitude expressed in degrees by 4 gives the equivalent time expressed in minutes.

Dividing the time, expressed in minutes, by 4 gives the equivalent longitude expressed in degrees.


Example - The difference in longitude between Chicago and San Francisco is 34 degrees.

What is the difference in time?
34x4 = 136 minutes; then: 136/60 = 2 hours and 16 minutes
 


Hydraulics

Doubling the diameter of a pipe increases the capacity four times.

Circular apertures are most efficient for discharging water, since they have less frictional surface for the same area.

To find the pressure in pounds per square inch of a column of water, multiply the height of the
column in feet by 0.434 (Approximately every foot of elevation is considered equal; to ½ lb. pounds per square inch). A one foot square, column of water, stacked 3.14 feet tall, equals a pressure of one pound per square inch.   

The time required to discharge equal quantities of water, under the same heads, through pipes of equal lengths, will be different for varying forms, and proportionally as follows: For a straight line, 90; for a true curve, 100; and for a right angle,140


                                                            MoMT









The Museum's effort to preserve the history of American Clocks and items which measure includes a compilation of short articles which address items featured in the museum. 


To continue this endeavor, the museum provides handouts of this information for museum visitors.  The articles are provided to assist in the explanation of items on exhibit in the museum. They are not intended to provide a detailed study of the subject. 


Visitors may obtain a copy of most of this information during their visit to the museum. 


This information is not copyrighted; however, some subjects and information contained in the articles may be protected by separate copyright. It is recommended that use of the information be for personal use.


Copies of this information are not be distributed without specific authorization from the Museum of Measurement and Time.


A list of almanac subjects is provided below. Copies are available when you visit the museum. Please make your request for specific information upon arrival.  For persons unable to visit the museum, written requests will be addressed on an individual basis. 


These articles are listed below. The subject will be changed periodically, so visit us often for the updates! 


ALMANIC  SECTION

LIST OF ALMANAC SUBJECTS

 SPECIAL INTEREST  


 Presidents Who Were Land Surveyors

Republic of Texas BoundarySurvey of 1841

History of Marion County, Texas

History of Jefferson, Texas



CLOCKS  OR  HOROLOGY


TimeLine of Measurement History

Major American Clock Makers

Rotation of the Earth

Latitude, Longitude & Time

Time Zones Around the World

The American Meridian

The Story of Longitude

The Gregorian Calendar

The Calendar Clock

The Industrial Revolution (Kitchen Clock)

The Clock and Compass Face 

The Story of Standard Time






 Almanac  Subject  Of  The  Day

​​​​​​​​​​​​Museum Of Measurement And Time

MEASUREMENT


​History of Land Ownership

History of Measurement & Measurement Devices

Land Surveying Units

Magnetic Compass

Magnetic North

True North

History of the Odometer

The Gunter Chain



CALCULATIONS


Napier's Rods & Bone

Logarithems

The Slide Rule

Tidbits of Math

Snippets of Math