arithmetics in forestry
TRANSCRIPT
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By
Jyothish J Ozhakkal
Roll No: 26 (FRO Trainee)
Arithmetics in Forestry
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Contents
Arithmetic operations
Powers & Roots
Ratio & Proportion
Simple Interest & Compound Interest
Logarithms
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Origin
From the Greek word arithmos - number
Arithmetic operations
Addition (+)
Subtraction ()
Multiplication ( or or *)
Division ( or /)
http://en.wikipedia.org/wiki/Numberhttp://en.wikipedia.org/wiki/Number -
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x: base
n: either integer or fraction
Powers and Roots
n
x
...
8)givewillcubed2(since28
555
3/1
4
2
bbbbb
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Powers and RootsAlgebraic Rules for Powers
Rule for Multiplication:
Rule for Division:
Rule for Raising a Power to a Power:
Negative Exponents: A negative exponent indicatesthat the power is in the denominator:
Identity Rule: Any nonzero number raised to thepower of zero is equal to 1, (xnot zero).
mnmn xx
mnmn xxx
mnmn xxx
n
n
xx 1
10 x
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RatioProportion - Fraction .
1 to every 2 is a Ratio
1 out of 3 is a Proportion
One third is a Fraction
Ratios comparePART WITH
PART
Proportionscompare PARTWITH WHOLE
Fractionscompare PARTWITH WHOLE
using shorthand
such as 1/3
3 different ways to
say the same thing
3 different ways to
compare numbers
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Ratio, Proportion or Fraction?
two out of five
This is a proportion
two fifths
This is a fraction
four tenths
This is a fraction
four to every ten
This is a ratioten to every four
This is a ratiofour out of ten
This is a proportion4/10
This is a fraction
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Simple Interest
Principal: An amount of money borrowed orloaned.
Interest: A charge for the use of money, paid bythe borrower to the lender.
Simple Interest: Interest paid only to theprincipal
Interest = Principal Rate Time
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Compound Interest
F - future value
IfP represents the present value
rthe annual interest rate
tthe time in years
n the frequency of compounding
F = P( 1 + r/n)nt
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Continuous Compounded Interest
Compound just every hour, or every minute orevery second or for every millisecond!
The future value formula is:F = Pert.
The annual yield for continuouslycompounded interest:
y = er 1.
e =2.7182818
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Logarithms
102 = 10010 raised to the power 2 gives 100
Base
IndexPower
ExponentLogarithm
The power to which the base 10 must be raised to give 100 is 2
The logarithm to the base 10 of 100 is 2
Log10100 = 2
Number
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Logarithms
102 = 100Base
Logarithm
Log10100 = 2
Number
Logarithm
Number
Base
y = bxLogby = x
23 = 8 Log28 = 3
34
= 81 Log381 = 4Log525 =2 5
2 = 25
Log93 =1/2 9
1/2 = 3
logby = xis the inverse of
y = bx
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103 = 1000 log101000 = 3
24 = 16 log216 = 4
104 = 10,000 log1010000 = 4
32 = 9 log39 = 2
42 = 16 log4
16 = 2
10-2 = 0.01 log100.01 = -2
log464 = 3 43 = 64
log327 = 3 33 = 27
log366 =1/2 36
1/2 = 6
log12
1= 0 120 = 1
p = q2 logqp = 2
xy = 2 logx2 = y
pq = r logpr = q
logxy = z xz = y
loga
5 = b ab = 5
logpq = r pr = q
c = logab b = ac
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103 = 1000 log101000 = 3
24 = 16 log216 = 4
104 = 10,000 log1010000 = 4
32 = 9 log39 = 2
42 = 16 log4
16 = 2
10-2 = 0.01 log100.01 = -2
log464 = 3 43 = 64
log327 = 3 33 = 27
log366 =1/2 36
1/2 = 6
log12
1= 0 120 = 1
p = q2 logqp = 2
xy = 2 logx2 = y
pq = r logpr = q
logxy = z xz = y
loga
5 = b ab = 5
logpq = r pr = q
c = logab b = ac
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103 = 1000 log101000 = 3
24 = 16 log216 = 4
104 = 10,000 log1010000 = 4
32 = 9 log39 = 2
42 = 16 log4
16 = 2
10-2 = 0.01 log100.01 = -2
log464 = 3 43 = 64
log327 = 3 33 = 27
log366 =1/2 36
1/2 = 6
log12
1= 0 120 = 1
p = q2 logqp = 2
xy = 2 logx2 = y
pq = r logpr = q
logxy = z xz = y
loga
5 = b ab = 5
logpq = r pr = q
c = logab b = ac
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103 = 1000 log101000 = 3
24 = 16 log216 = 4
104 = 10,000 log1010000 = 4
32 = 9 log39 = 2
42 = 16 log4
16 = 2
10-2 = 0.01 log100.01 = -2
log464 = 3 43 = 64
log327 = 3 33 = 27
log366 =1/2 36
1/2 = 6
log12
1= 0 120 = 1
p = q2 logqp = 2
xy = 2 logx2 = y
pq = r logpr = q
logxy = z xz = y
loga
5 = b ab = 5
logpq = r pr = q
c = logab b = ac
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103 = 1000 log101000 = 3
24 = 16 log216 = 4
104 = 10,000 log1010000 = 4
32 = 9 log39 = 2
42 = 16 log4
16 = 2
10-2 = 0.01 log100.01 = -2
log464 = 3 43 = 64
log327 = 3 33 = 27
log366 =1/2 36
1/2 = 6
log12
1= 0 120 = 1
p = q2 logqp = 2
xy = 2 logx2 = y
pq = r logpr = q
logxy = z xz = y
loga
5 = b ab = 5
logpq = r pr = q
c = logab b = ac
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Laws of logarithms
Every number can be expressed in exponentialform every number can be expressed as a log
Let p = logax andq = logay
So x = apandy = aq
xy = ap+q
p + q = loga(xy)
p + q = logax + logay = loga(xy)
loga(xy) = logax + logay
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Laws of logarithms
Every number can be expressed in exponentialform every number can be expressed as a log
Let p = logax andq = logay
So x = apandy = aq
xy = ap-q
p - q = loga(x/y)
p - q = logax - logay = loga(x/y)
loga(x/y) = logax - logay
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Laws of logarithms
Every number can be expressed in exponentialform every number can be expressed as a log
Let p = logax andq = logax
So x = apandx = aq
x2 = ap+q
p + q = loga(x2)
p + q = logax + logax = loga(x2)
logaxn = nlogax
L f l i h
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Laws of logarithms
Every number can be expressed in exponentialform every number can be expressed as a log
loga(x/y) = logax - logay
loga(xy) = logax + logay
logaxn = nlogax
am.an = am+n
am/an = am-n
(am)n = am.n
Ch f b
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Change of base property
Logax =Logbx
Logba
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Our final concern then is to
determine why logarithms like the
one below are undefined.
Can anyone give us
an explanation ?
2log ( 8)
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One easy explanation is to simply rewritethis logarithm in exponential form.Well then see why a negative value is not
permitted.
First, we write the problem with a variable.
2y
8 Now take it out of the logarithmic form
and write it in exponential form.
What power of 2 would gives us -8 ?
23
8 and 2 3
1
8
Hence expressions of this type are undefined.
2log ( 8) undefined WHY?
2log ( 8) y
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FOREST NURSERY
Seed Purity Percentage = Weight of Pure seed x100
Total weight of sample
Seed Moisture Percentage = Weight of moisture x100
Weight of moisture + dry matterweight
Quantity of seeds req. for raising plantation = A x DKgs
S x N x G x P x M
(A-area to be planted, D-density of plantation, S-survival %,N-no. of seeds per Kg, G-Germination %, P-purity of seed,
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PLANTATION FORESTRY
Method of calculating number of plants per hectare
Line method = 100 x 100 x Area in hectare
Line to line distance x plant to plant distance
Square method = 100 x 100 x Area in hectare
Square of the planting distance
Triangular method = 100 x 100 x 1.155 x Area in
hectareSquare of the planting distance(side of the
triangle)
Quincunx method = 100 x 100 x 2 x Area inhectare
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The Fibonacci NumbersThe number pattern that you have been using is known as the
Fibonacci sequence.
1 1
}+
2
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The Fibonacci NumbersThe number pattern that you have been using is known as the
Fibonacci sequence.
1 1 2
}+
3
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The Fibonacci NumbersThe number pattern that you have been using is known as the
Fibonacci sequence.
1 1 2 3
}+
5 8 13 21 34 55
These numbers can be seen in many natural situations
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Fibonaccis sequence in nature
1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584
On many plants, the number of petals is aFibonacci number:
Buttercups have 5 petals; lilies and iris have 3petals; some delphiniums have 8; corn marigoldshave 13 petals; some asters have 21 whereas daisiescan be found with 34, 55 or even 89 petals.
13 petals: ragwort, corn marigold, cineraria, somedaisies21 petals: aster, black-eyed susan, chicory34 petals: plantain, pyrethrum55, 89 petals: michaelmas daisies, the asteraceaefamily.
Some species are very precise about the number ofpetals they have - eg buttercups, but others havepetals that are very near those above, with theaverage being a Fibonacci number.
Pairs
http://affiliates.allposters.com/link/redirect.asp?aid=910266&item=376240 -
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Pairs
1 pair
At the end of the first month there is still only one pair
Pairs
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Pairs
1 pair
1 pair
2 pairs
End first month only one pair
At the end of the second month the female produces anew pair, so now there are 2 pairs of rabbits
Pairs
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Pairs
1 pair
1 pair
2 pairs
3 pairs
End second month 2 pairs of rabbits
At the end of thethird month, theoriginal femaleproduces a second
pair, making 3 pairsin all in the field.
End first month only one pair
Pairs
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Pairs
1 pair
1 pair
2 pairs
3 pairsEnd third month3 pairs
5 pairs
End first month only one pair
End second month 2 pairs of rabbits
At the end of the fourth month, the first pair produces yet another new pair, and the femaleborn two months ago produces her first pair of rabbits also, making 5 pairs.
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1
1
2
3
5
8
13
21
34
55
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Fibonacci in Nature
The lengths of bones in a handare Fibonacci numbers.
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The Golden Ratio
The Golden (or Divine)Ratio has been talkedabout for thousands of
years.
People have shown thatall things of great beautyhave a ratio in theirdimensions of a number
around 1.618
1
1.618
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55+89 = 14434+55 = 89
21+34 = 55
13+21 = 34
8+13 = 21
5+8 = 13
3+5 = 8
2+3 = 5
1+2 = 3
1+1 = 2
ratio
1.6181.618
1.618
1.6191.615
1.625
1.61.666
1.5
The ratio of pairs of Fibonacci numbers gets closer to thegolden ratio
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The Golden Ratio
Leonardo da Vinci showedthat in a perfect man therewere lots of measurementsthat followed the GoldenRatio.
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