Alternate Method for Adding TimeDate: 02/09/2001 at 19:08:06 From: Siri Subject: Siri Factor use in time conversion formulae To: Dr. Math, I have found a factor to be used in a formula to make calculations easy (it is like math made easy). My school and others have been using the method. It has been published in the school magazine and has aired on TV stations. My dad sent it in my name to be trademarked and named after me (the Siri Factor). The trademark is pending. If you are interested in publishing it, I can send the details of the Siri Factor and Formula so that whole world will know about it. Please let me know, so that I can ask my dad to send to you. Date: 02/12/2001 at 17:55:13 From: Doctor TWE Subject: Re: Siri Factor use in time conversion formulae Hi Siri and Janardhan - thanks for writing to Dr. Math. I am a colleague of Dr. Ian, and I saw your initial posting this morning. Ian shared the message copied below with me, and I told him that I'd respond to you. From: Janardhan To: Dr. Ian Subject: Siri Factor Date: Mon, 12 Feb 2001 11:56:50 -0800 SIRI FACTOR (40) The Siri Factor is a constant number, 40. This Factor is named for my first name, Siri. I am 11 years old and I invented this factor to use in the formula described below. The Siri Factor (40) can be used to make mathematical calculations involving the time units hours, minutes and seconds easier. Calculations involving time units can be done easily by using the Siri Factor in a decimal-like format. Formula: A +/- B = C (minutes or seconds in A&B > 60) +/- Siri Factor (40) Addition: A + B (minutes/seconds or hours/minutes) = C + Siri Factor (40) (If the total number of minutes in A and B exceed 60) Subtraction: A - B (minutes/seconds or hours/minutes) = C - Siri Factor (40) (If the minutes in B exceed the minutes in A) Example: Suppose A = 3 hours, 40 minutes and B = 1 hour, 50 minutes. Adding A to B: 3:40 + 1:50 = 4:90 + Siri Factor (:40) = 5:30 (5 hours, 30 minutes) Subtracting B from A: 3:40 - 1:50 = 1:90 - Siri Factor (:40) = 1:50 (1 hour, 50 minutes) IMPORTANT FACTS: 1. The Siri Factor, 40, is a constant. 2. This Factor provides a simpler way of calculating time units when compared to conventional ways that involve additional steps. 3. Time units of hours and minutes in the above examples can be substituted with minutes and seconds. 4. This factor can also be used in multiple additions and subtractions of time units, by adding or subtracting the Siri Factor as necessary. 5. The Siri Factor can also be used in the calculation of multiplication and division of time units. Siri, 11 years old, 6th Grader --------------------------------- First, let me congratulate you, Siri, on a very clever mathematical insight. Most 11-year-olds would not come up with ways to make a tricky task like this easier. Well done! The idea, however, is not new - although applying it to sexagesimal (hours-minutes-seconds or degrees-minutes-seconds) calculations *may* be new. A similar technique, using what is commonly called a "decimal adjust" or "fudge factor," is used when calculators and computers add or subtract decimal numbers directly. Let me explain how your Siri Factor works mathematically, and then I'll explain how this relates to the computer's "fudge factor." For reference, let's assume we are dealing with hours and minutes, although the same logic holds for minutes and seconds. When you change a time value from, for example, 5:37 (h:mm) to 5.37 (decimal), you are changing the minutes from 1/60ths of an hour to 1/100th of an hour. Now let's add 5:37 and 2:48... "Traditional" way With Siri Factor ----------------- ---------------- 5:37 5.37 + 2:48 + 2.48 ------ ------ In both cases, we first add the units digit of the minutes. 7+8 = 15, so we record 5 and carry the 1. There is no difference here because both systems require 10 for a carry here. So we have: "Traditional" way With Siri Factor ----------------- ---------------- 1 1 5:37 5.37 + 2:48 + 2.48 ------ ------ 5 5 Next, we add the tens digits: "Traditional" way With Siri Factor ----------------- ---------------- 1 1 5:37 5.37 + 2:48 + 2.48 ------ ------ :85 .85 Then we add the hours: "Traditional" way With Siri Factor ----------------- ---------------- 1 1 5:37 5.37 + 2:48 + 2.48 ------ ------ 7:85 7.85 In both cases, we have to examine our results. With the traditional method, we see that we have 85 minutes, and we realize that we can't go above 60. So we subtract 60 minutes and add 1 hour. With the Siri method, we also realize that we added more than 60 minutes, so we add the Siri Factor, .40 "Traditional" way With Siri Factor ----------------- ---------------- 1 1 5:37 5.37 + 2:48 + 2.48 ------ ------ 7:85 7.85 - :60 + .40 ------ ------ 7:25 8.25 + 1:00 ------ 8:25 In both cases, we end up with 8:25. We can shorten the "traditional" method a bit by making the correction immediately as we add the minutes. When we add the tens digits of the minutes, we get 1+3+4 = 8. But 6 tens of minutes (i.e. 60 minutes) make an hour, so we make 6 of our 8 a carry and record the remaining 8-6 = 2. Modified traditional way ------------------------ 1 1 <- the carry into the hours represents 6 groups of 5:37 10 minutes + 2:48 ------ :25 Now we add the hours (with the carry from the tens of minutes) and we have: Modified traditional way ------------------------ 1 1 5:37 + 2:48 ------ 8:25 The difference between these methods is in the carry from the tens of minutes to hours. In the modified traditional way (and essentially in the traditional way - though more indirectly), we carry a group of 6 tens to make an hour. In the Siri method, we carry the normal 10 tens of the decimal system. However, because the result (.85 in the example) is not valid, we add the Siri factor of .4. This makes the group of 6 tens that should have been carried into a group of 10 tens that are carried. Subtraction works similarly, reducing a borrow of 10 tens into the required borrow of 6 tens. The Siri Factor takes away the extra 4. As I mentioned earlier, calculators and computers use a similar technique when they add decimal numbers directly. Calculators and computers traditionally work in binary, or base 2, because they use tiny electronic "on/off switches" to represent the 1's and 0's. However, when dealing with larger numbers, it is easier to think of them as working in hexadecimal, or base 16. If you are not familiar with other bases - and binary and hexadecimal in particular - you may want to check out our "Number Bases" FAQ at: http://mathforum.org/dr.math/faq/faq.bases.html Suppose a calculator is used to add 38 and 77 without converting them to hexadecimal. It will start by adding the units digits, 8+7 = 15. But in hexadecimal, 15 is a valid digit and is represented by an F. So the calculator will have: 38 + 77 ---- F Next, the calculator will add the "tens" digits (actually, they are sixteens digits in hexadecimal), 3+7 = 10. Again, 10 is a valid digit in hexadecimal and is represented by a A. So the calculator now has: 38 + 77 ---- AF Of course, AF is not a valid decimal answer (just as 7:85 was not a valid time answer), so the calculator adds a "fudge factor" of 6. First, it adds 6 to the units (because F is an invalid units digit). F+6 = 15 in hexadecimal (15+6 = 21): 38 + 77 ---- 1 <- carry from the units when adding the fudge factor AF + 6 ---- B5 Next, it adds 6 to the tens (because B is an invalid tens digit). B+6 = 11 in hexadecimal (11+6 = 17): 38 + 77 ---- 1 AF + 66 ---- 115 And thus it gets the correct answer. Why was the fudge factor 6? Because that makes the 10 ones that we should have carried over to the next digit into a group of 16 ones that the calculator does carry over in hexadecimal. When is the fudge factor of 6 used? When either [a] a digit is greater than 9 (and thus invalid in decimal), or [b] a carry is generated from that digit. In case [a], the fudge factor is needed to make a group of 10 that should be carried a group of 16 that will be carried. In case [b], the fudge factor is needed to "give back" the extra 6 that were carried (the calculator carried 16, when it should have only carried 10). Looking at how calculators handle decimal numbers, I would not be surprised if those calculators that have the capability to add and subtract sexagesimal (DMS) values don't already use the Siri Factor - but I'm not sure. I haven't explored how they handle DMS calculations. If I discover this, I'll write you back. One final thought on the Siri Factor: Like the fudge factor above, you have to be careful to be sure to use it properly. Consider the following two additions: 1:55 2:05 + 2:50 + 2:00 ------ ------ Using the Siri method: 1 1.55 2.05 + 2.50 + 2.00 ------ ------ 4.05 4.05 Just looking at the results, both look valid and we can't tell whether they need a Siri Factor added on. The first one needs a Siri Factor (because of the carry into the hours), but the latter does not. So to use the Siri Factor properly, you have to examine what you're doing - and I'm not sure that it's *significantly* simpler that just doing it the old fashioned way. Again, congratulations on your work - you definitely have the attitude to become a renowned mathematician! - Doctor TWE, The Math Forum http://mathforum.org/dr.math/ Date: 05/14/2007 at 13:06:16 From: Jack Subject: The Siri Factor Siri's method has been known to surveyors, as the following web page indicates: http://www.fer3.com/arc/m2.aspx?y=200302&i=009016 Date: 05/14/2007 at 21:28:43 From: Doctor Rick Subject: Re: The Siri Factor Thanks, Jack, that's interesting. Even if the method has been known before Siri discovered it, it's still pretty neat that an 11-year old would come up with that insight. - Doctor Rick, The Math Forum http://mathforum.org/dr.math/ |
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