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Prologs at Glanusk Horse Trials

Lec, an Eventing Nation regular and guest writer from the UK, attended the Glanusk horse trials over the weekend.  Lec sent us this report with her thoughts and observations about Prologs, which are styrofoam logs that you might remember reading about in our Rolex coverage.  Thanks for writing this lec and thank you for reading.  

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From lec:


This weekend saw the very first Glanusk International Horse Trials in the UK. Running levels from Novice, Training, Prelim, Intermediate and CCI 1*.

 

This was the first event in the UK that was trialling polystyrene logs - Prolog. I was lucky enough to chat to the fence judges, Eric Winter the course designer and Canadian eventer Mike Winter who designed the Prolog and who was watching and videoing the fence to see how it jumped.

 

 

The fence had an upright log going into the water and then up a small mound to the second upright log. Both of these fences were made of Prolog. The fence judge told me that in the Intermediate it had been riding horribly and riders seemed to be taking far too many risks into the fence. Three riders had snapped the fence out of about 40 entries in the Intermediate. The fence judge was not convinced by these fences as they had seen some bad riding. Several of these were experienced pros and felt that people did not have the respect they should have had for it.


Links: Glanusk homepage, WFP's Glanusk recap, Prolog site 

 

Snapped logs.

 

I asked Mike Winter why this was happening and it appears that one horse completely breasted it when coming in far too fast, another horse had left a leg and another had stopped but went through the fence. Mike Winter was of the opinion that by using the Prolog it has stopped a rotational fall. Mike has video of the fence which I am hoping to get a copy of in order to post on EN.

 

Look at all the marks on the log.

 

The same fences had been in the 1* but nobody had snapped them. The main difference between the 1* and the Intermediate was that the course was roped differently. The 1* approached the fence straight while the Intermediate riders came off a turn.

 

Another factor is that they made a change for the Intermediate in the posts holding the fence up. In the 1* it should have collapsed but did not so they cut away to make it break. On this photo you can see where they have cut away more from the posts.

 

Interestingly at BE events there are no penalties for breaking the log but the fence judge has the discretion to give penalties if the horse has stopped then broken the log. 

 

Eric Winter is a designer who builds bold courses and one of the influences you could clearly see on his course was the open corners that we saw at Badminton. Eric took over Blenheim 3* two years ago and I expect to see him design 4* courses very soon. All his courses are very horse friendly but scare the rider and need attacking.


 

Lots of the fences had frangible pins.

 


This is a brand new course so for me it was interesting to see what direction course designers are taking. All the levels were big and bold. This seems to be the fashion at the moment in the UK where riders have to really kick and be brave. I understand there will be a feedback session from the Prolog so it will be interesting to see what the consensus is.

11 Comments

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excellent Lec!!
The jump judges opinion is VERY interesting. A jump judge at a water jump is ALWAYS a very experienced judge so their thinking that riders did not show respecet is very very interesting. hmmmmmmmmmmm

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maybe it wasn't about the riders having enough respect for the prolog.. maybe the fence was not positioned very well on course?

Thanks for writing this lec. Do you think the judges meant that the riders were not respecting the prologs *because* they were prologs? Or was it just bad riding for some reason?
Its going to be so hard to say for sure, because how can we know if these breaks would have caused falls without the logs, and how can we know if the mistakes would have been the same without the logs?
Please keep us posted!

I've read several arguments for and against (if that's how you want to put it) these types of jumps (frangible pins, collapsible logs, etc). Not being an upper level rider I cannot say which I would prefer if I were running a course like this. My thought is that these collapsible logs make horses less careful - if a horse rubs a solid fence and feels that there is no give, he will be careful not to rub on the next one if he is shrewd. If a horse rubs a log that has some give and bounce to it, he may begin to take the jumps' size for granted and get lazy. Now, I am not arguing against safety by any means - the safer these courses can be and the less rotational falls there are the better of course - I am just concerned that both horse and rider will begin to get lazy with their technicality and pace, knowing that a mistake that would not have passed in a previous course would be allowed now. Please take my words with a grain of salt as I am definitely in favor of these types of jumps I would just hope that the riders and horses continue to train as if the jumps were not made of foam and ensure that they had a technically clean and safe ride through XC.

Could someone explain to me how riders 'don't respect' a fence? If the riders have no experience of how a Prolog takes a hit, it seems unlikely that they would ride carelessly into it (especially if it's a drop into water). If horses have no experience of a Prolog, it seems unlikely that they would say 'Oh that one's styrofoam' and whack their legs on it. In both cases, horses and riders are used to seeing solid logs and jumping them like solid fences.

The situation at the water fence sounds remarkably similar to a situation that occurred at an Intermediate log-into-water at one of the southeast US events this year. The log had to be replaced several times and numerous horses hit it. It's definitely worth investigating if the same thing is happening at similar 'new' fences on both sides of the Atlantic.

One of the theories that was mentioned to me was that in the Intermediate the horses could see the water when they came round the water and then did not take their eye off it and left a leg, whereas in the 1* they approached straight and so this problem did not happen. I would be very interested to know if this is similar to the issues faced at Rolex over the log to steps down as the horses seemed to spot the steps and then leave a leg at the log on the top. I will definitely try and get the videos then you can judge for yourself about the way riders approached the fence. Eric Winter questioned whether they were just lower class horses but a fair few had qualified for 3* and 4* that were going round they were not just green intermediate horses.

All respect to the Winter's, but it seems a bit fishy to me to question the horses at an event in the UK. I would think that at *any* I level event there would be some A horses that were taking a break, schooling, etc, and some greener horses new to the level, and that course designers plan for that. I'm not sure it is fair to blame the horses- it is rarely the horse's fault, as we all know!

I HATE open corners!

Ditto JER!!!!! =)!!!

I've figured out how I wanted my blog layout and everything, it's just that other blogs that I've visited that use Blogspot have nice big headers. Mine is just text, so can someone enlighten me on how to make a pretty header?.


109 Theorem is not a straight line along the same line of three points determine a circle.
110 vertical diameter perpendicular to the chord of the diameter of Theorem split this string by string and split on two arcs
111 Corollary 1


What this triangle is right triangle

two segments long the proportion of items
133 deduced from outside the circle round the two secant point lead, which is the secant and the circle of intersection of each of the two line


body (content) product unit conversion
1 cubic meter = 1000
1 cubic decimeter cubic decimeter = 1000 cubic centimeters
1 cubic decimeter = 1 liter
1 立方厘米 = 1 ml
1 cubic meter = 1000 l

heart strings of string from the same
; 115 deduction in the same round and round, or, if the two central angle, two arcs, or two strings from two strings of the heart strings

--- shop59015483. taobao.com




1, each = total number of the total number of shares × ÷ ÷ total number of copies of each number = number of copies of each
2 = , 1 × multiplier = multiplier times the number of times the number of ÷ 1 ÷ multiple = multiple times the number of multiples of multiples = 1
3, distance = speed × time = distance ÷ speed Time time = distance ÷ speed
4, unit price × quantity = total price = total price ÷ ÷ total number = unit number
5, the efficiency of work × hours = total work efficiency = total ÷ total hours of work ÷


formula

; the edges are equal (isometric to the other side)
35 Corollary 1 three angles are equal The triangle is an equilateral triangle
36 Corollary 2 has an angle of an isosceles triangle is equal to 60 ° equilateral triangle
; 37 in a right triangle, if one acute angle is 30 ° so that it is equal to the hypotenuse of a right-angle side of half
38 on the hypotenuse the center line on the hypotenuse is equal to half the
39 Theorem perpendicular bisector of line segment and this segment of points equidistant from the two endpoints
; 40 converse and a line equidistant from the two end points in this segment of the vertical bisector
41 the perpendicular bisector of line segment and the segment end points can be regarded as equal to the distance set of all points
42 Theorem 1 on a straight line is the symmetry of the two graphics congruent shape
43 Theorem 2 If two graphics symmetrical about a straight line, then the axis of symmetry is the vertical level corresponding to point connection

cosA + cosB = 2cos ((A + B) / 2) sin ((AB) / 2)
tanA + tanB = sin (A + B) / cosAcosB tanA-tanB = sin (AB) / cosAcosB
ctgA + ctgBsin (A + B) / sinAsinB-ctgA + ctgBsin (A + B) / sinAsinB

some series before n items and
1 +2 +3 +4 +5 +6 +7 +8 +9 + ... + n = n (n +1) / 2 ; 1 +3 +5 +7 +9 +11 +13 +15 + ... + (2n-1) = n2
2 +4 +6 +8 +10 +12 +14 + ... + (2n) = n (n +1) 13 +23 +33 +43 +53 +63 + ... n3 = n2 (n +1) 2 / 4

and poor problem formulation
(and + poor) ÷ 2 = large number
(and - worse) ÷ 2 = decimal

bad times worse problem
÷ (factor -1) = decimal
; decimal × multiplier = large numbers
(or decimal + SD = large numbers)

and a right angle is proportional to the corresponding side, then the two triangles similar to the 96 triangles correspond to the nature of Theorem 1 is similar to the high ratio, corresponding to the center line than the corresponding angle bisector than both

encounter problems
encounter distance = speed × time
meet encounter time = distance ÷ speed and
meet the speed and distance ÷ = meet meet Time

ratio, then this straight line parallel to the triangle's third side
89 parallel to the side of the triangle, and the other on both sides of the intersection of the straight line intercepted by the triangle's three sides

intercepted on the other line segments are equal
79 Corollary 1 after the midpoint and trapezoidal back end of a parallel line, will split the other waist
80 Corollary 2 through the side of the midpoint of the triangle and the other side parallel lines, will split the third side
81 Theorem triangle triangle median line median line parallel to the third side and equal to its half of the 82 Theorem trapezoid trapezoidal median line median line parallel to the two bottom and two at the end and is equal to half of L =


downstream water problems


point of helping children to find their own things, it is estimated to friends and some also use the space on the good things we share, even though take it!

any acute angle of the tangent is equal to its complementary angle of the cotangent value, the cotangent value of any acute angle is equal to its complementary angle

area unit conversion
1 square km = 100 hectares
; 1 hectare = 10,000 square meters
1 square meter = 100 square decimetres
; 1 square decimeter = 100 cm2
1 平方 cm = 100 mm2

shape symmetrical about this line
Pythagorean triangle two sides at right angles 46 a, b and the square is equal to the square of the hypotenuse c,

profit and loss issues
(profit + loss) ÷ volume of distribution of the difference between the two = to participate in the distribution of copies
(large surplus - a small profit) ÷ = ​​twice the difference between the amount allocated to participate in the distribution of copies
(burned - small loss) ÷ = ​​twice the difference between the amount allocated to participate in the distribution of copies



line should be proportional to
88 Theorem If a line cut both sides of the triangle (or both sides of the extension cord) from the corresponding segments into

; a3-b3 = (ab (a2 + ab + b2)
triangle inequality | a + b | ≤ | a | + | b | | ab | ≤ | a | + | b | | a | ≤ b -b ≤ a ≤ b
; | ab | ≥ | a | - | b | - | a | ≤ a ≤ | a |
solution of a quadratic equation-b + √ (b2-4ac) / 2a-b-√ (b2- 4ac) / 2a
relationship between roots and coefficients of X1 + X2 =- b / a X1 * X2 = c / a Note: Vedic Theorem

discriminant
b2-4ac = 0 Note: The equation has two equal real roots
b2-4ac> 0 Note: The equation has two unequal real roots
; b2-4ac
formula

; (b + d + ... + n) = a / b
86 parallel line segments proportional to the theorem of three sub-parallel lines cut two straight lines, proportional to the corresponding segments from
87 inference line parallel to the side of the triangle cut other side (or both sides of the extension cord), obtained on the


All primary school to junior high school mathematics


Weight unit conversion

moldings split a diagonal
71 Theorem 1 on the central symmetry The two graphics are congruent
72 Theorem 2 on the central symmetry of the two graphs, symmetry point connections are through the center of symmetry, and is on the said center split
73

converse if the corresponding two graphics point connections are through a point, and this split is that


ratio term
; 132 theorems from the cutting line a little outside the circle tangent and secant cited circle, tangent to the secant long is this intersection with the circle

profit and discounts
profit = selling price - cost margin = Profit ÷ Cost × 100% = (selling price ÷ cost -1) × 100%
; Change Change amount = principal × the percentage of the actual selling price = ÷
discount the original price × 100% (discount Interest = principal × rate × time
after-tax interest = principal × rate × time × (1-20%)

length unit converter
1 km = 1000 m 1 meter = 10 decimeter
1 decimeter = 10 cm 1 meter = 100 centimeters
; 1 cm = 10 mm


time unit conversion
1 century = 100 years 1 year = 12 months big month (31 days): 1 3 5 7 8 10 December
; Satsuki (30 days) are: 4 6 9 November
February 28 leap year day, leap year, February 29 天
average year 365 days, leap year 366 days
1 day = 24 hours 1 hour = 60 minutes
1 min = 60 seconds, 1 hour = 3600 seconds

Primary Mathematics geometry perimeter area volume formula

1, rectangular perimeter = (length + width) × 2 C = (a + b) × 2
2, square perimeter = side × 4 C = 4a
3, the rectangular area = length × width S = ab
4, area = side of square length × side length S = aa = a
5, the area of ​​a triangle = base × height ÷ 2 S = ah ÷ 2
6, the area of ​​parallelogram = base × height S = ah
7, the area of ​​trapezoid = (on under the bottom end +) × high ÷ 2 S = (a + b) h ÷ 2
8, diameter = radius × 2 d = 2r radius = diameter ÷ 2 r = d ÷ 2
9, circumference of a circle = pi × diameter = pi × radius × 2 c = πd = 2πr
; 10, circle area = pi × radius × radius

common middle school math
1 and only had two points a straight line between two points
2 line with the shortest
3 of supplementary angle equal to angle or isometric
4 with angle or The complementary angle equal
5 isometric point and only had a straight vertical line and the known
; 6 point outside a straight line and straight line segments to connect all the points in the vertical section of the shortest
7 point outside a straight line through the parallel axiom, there and Only a straight line parallel with this line if two lines are
8 and a third line parallel to the two lines are parallel to each other
; 9 corresponding angles are equal, the two straight lines parallel to the
10 interior angles are equal, the two straight lines parallel to the
11 with the next complementary angles, two straight lines parallel to the two parallel
12, corresponding angles are equal
; 13 two parallel lines, interior angles are equal
14 two straight lines parallel with the side angles complementary
; 15 on both sides of the triangle theorems and inference than the third side
16 on both sides of the triangle is less than the third side
; 17 angles of a triangle three angles of a triangle theorems and deduction equal to 180 °
18 1 right triangle the two acute Corollary 2 each I
19 exterior angle is equal to a triangle and its two non-adjacent interior angles and
20 Corollary 3 a triangle exterior angle is greater than any one and it is not adjacent angles of congruent triangles correspond
21 side, corresponding angles are equal
22 corners while axiom (SAS) with both sides and the angle between them equal to the corresponding two triangles congruent
23 angle corner axiom (ASA) with corners and edges corresponding to the same folder they are the two triangles congruent
; 24 inference (AAS) with corners and edges which correspond to the same corner of the two triangles congruent
25 Collage side axiom (SSS) has three sides congruent triangles correspond to two equal
26 bevel, right angle side axiom (HL) with bevel edge and a right-angle equal to the corresponding The two right triangles congruent
27 Theorem 1 in the angle bisector of this angle on both sides point to the same distance
; 28 Theorem 2-1 from the same angle on both sides of the point, in this corner of the angle bisector
29 to the angle bisector is equidistant from both sides of the set of all points
30 isosceles triangle isosceles triangle theorem of the nature of the two bottom corners are equal (ie, equilateral on isometric)
31 Corollary 1 isosceles triangle angle bisector and perpendicular to the bottom split bottom
32 isosceles triangle the angle bisector, middle and bottom edge of the bottom edge of the high overlap each other inference
33 3 equilateral triangle all angles are equal, and each angle is equal to 60 °
34 isosceles triangle theorems to determine if a triangle has two angles are equal, then the two angles are right

equal amount in a group if they correspond to the amount of the other groups are equal ;
116 Theorem an arc of the circumference of the angle of the central angle is equal to its half
117 Corollary 1 with the other arc of the arc or angle equal to the circumference; and round the same circle or in equal circumferential angle of the right

that a ^ 2 + b ^ 2 = c ^ 2
47 Pythagorean triangle's three sides if the converse long a, b, c have the relationship a ^ 2 + b ^ 2 = c ^ 2, then


① split string (not diameter) of the diameter perpendicular to the strings, and split the string by two arcs of
② perpendicular bisector of chord through the center of the circle, and split the string by two arcs of
; ③ split the string by an arc of diameter, the vertical split strings, and split a string by another arc of inference
112 2 round clip of two parallel chords of the circular arc equal
113 center as a center of symmetry is the center of symmetry
; 114 Theorem and round the same circle or in equal central angle of the arc of the same, the equivalent of the string, the right


sine
100

arc are equal
118 Corollary 2 semi-circular (or diameter) of the circumference of the angle is right angle; 90 ° of the circumferential angle of the chord is the diameter of Corollary 3 If
119 midline on the side of a triangle is equal to half the side, then the triangle is right angle

sub-line
44 Theorem 3 symmetrical two graphics on a straight line, or if they extend the line of the corresponding segments intersect, then



multiplication and factoring a2-b2 = (a + b) (ab) a3 + b3 = (a + b) (a2-ab + b2)

triangle
; 120 Theorem circle inscribed quadrilateral diagonal complementary, and any exterior angle is equal to its diagonal
121 ① in a straight line intersects the d L and ⊙ O ② ⊙ O tangent line L, and d = r
③ straight line L and ⊙ O phase from the d> r
122 Tangent Theorem to determine the radius of the outer end and through the vertical at this radius of the circle tangent line is tangent to the nature of Theorem
123 round through the cut perpendicular to the tangent point of radius
Corollary 1 and 124 through the center perpendicular to the tangent line will pass through cut-off point
125 Corollary 2 after cut-off point and the line will be perpendicular to the tangent After a long Theorem center
126 from outside the circle tangent point lead two tangent circles, their looks, etc. tangent, the center and the


working hours = productivity
; 6, addend + addend = and and - a one addend = addend
7, minuend - subtrahend = difference minuend - bad + bad = subtrahend subtrahend = minuend
8, plot plot factor × factor = ÷ a factor of = another factor ;
9, dividend ÷ divisor = business = Business dividend ÷ divisor = dividend divisor provider ×


Primary Mathematics graphic formula

tangent
101 round is a distance equal to the fixed length set of points inside the circle
102 can be seen as the center point of the distance is less than the radius of the circle set
103 outside can be seen as the distance is greater than the radius of the center point of the set
104 or so round the circle with radius equal to
; 105 a distance equal to the fixed point of the trajectory of fixed length, is designated as the center circle of radius length and the known line two
106 equal distance from the end point of the track, is the perpendicular bisector of segment
107 to a known angular distance equal points on both sides of the track, is the angle bisector
108 到 two parallel lines equidistant from the locus of points, and two parallel lines are parallel and equidistant one

weight + weight of solvent = solution weight ÷ solution of the weight of the solute weight × 100% = weight × concentration of solution concentration
= weight of the solute concentration
solute = solution weight ÷ weight

corners and formulas
sin (A + B) = sinAcosB + cosAsinB sin (AB) = sinAcosB-sinBcosA
cos (A + B) = cosAcosB-sinAsinB cos (AB) = cosAcosB + sinAsinB tan (A + B) = (tanA + tanB) / (1-tanAtanB) tan (AB) = (tanA-tanB) / (1 + tanAtanB )
ctg (A + B) = (ctgActgB-1) / (ctgB + ctgA) ctg (AB) = (ctgActgB +1) / (ctgB- ctgA)

fold angle formula
tan2A = 2tanA / (1-tan2A) ctg2A = (ctg2A-1) / 2ctga
cos2a = cos2a-sin2a = 2cos2a-1 = 1-2sin2a

; half-angle formulas
sin (A / 2) = √ ((1-cosA) / 2) sin (A / 2) =- √ ((1-cosA) / 2)
cos (A / 2) = √ ((1 + cosA) / 2 ) cos (A / 2) =- √ ((1 + cosA) / 2)
tan (A / 2) = √ (( 1-cosA) / ((1 + cosA)) tan (A / 2) =- √ ((1-cosA) / ((1 + cosA))
ctg (A / 2) = √ ((1 + cosA) / ((1-cosA)) ctg (A / 2) =- √ ((1 + cosA) / ((1-cosA))
and poor of the plot
2sinAcosB = sin (A + B) + sin (AB) 2cosAsinB = sin (A + B)-sin (AB)
2cosAcosB = cos (A + B)-sin ( AB)-2sinAsinB = cos (A + B)-cos (AB)
sinA + sinB = 2sin ((A + B) / 2 ) cos ((AB) / 2

equal to the product of long section
; 134 if the tangent to two circles, then cut point must be in line with the heart outside the circle
135 ① two from d> R + r ② outer two circles cut d = R + r
③ two circles intersect Rr r)
④ two circle cut d = Rr (R> r) ⑤ two circles containing d r)
; 136 Theorem intersection of two circles with the center line perpendicular bisector of two circles theorems public string
137 into the circular n (n ≥ 3): ⑴ in turn link the points from the polygon is the circle inscribed regular n-gon
; ⑵ through the points for the circle tangent to the intersection of tangent adjacent vertices of the polygon is outside the circle


converse 45 points if the two corresponding connection graph is a straight line with a vertical split, then the two plans


1 ton = 1000 kg
; 1 kg = 1000 g = 1 kg
1 千克

planting questions
1, non-closure of the main line on the issue of tree planting can be divided into the following three scenarios:
⑴ If the non-closed tree-planting at both ends of the line, then:
; number of trees = number of segments + 1 = length ÷ spacing -1
; length = spacing × (number of plant -1)
spacing = length ÷ (number of plant -1)
; ⑵ If the non-closed one end of the line to plant trees, not planted the other end, then:
number of trees = number of segments = length = length ÷ spacing
spacing × number of trees
spacing = length ÷ number of trees
⑶ If the line ends in a non-closed are not trees, then:
number of trees = number of segments -1 = length ÷ spacing -1
length = spacing × (number of trees +1)
spacing = length ÷ (number of trees +1)


equal to the similar ratio 97 properties similar to Theorem 2 is similar to a triangle is equal to the ratio of the circumference than
98 nature of the similar triangles theorem 3 area ratio is equal to the square of
99 similar than the sine of any acute angle is equal to the cosine of its complementary angle, the cosine of any acute angle is equal to its complementary angle

the original triangle into a triangle similar to
91 similar triangles to determine the Theorem 1 ; corners correspond to the same, the two triangles are similar (ASA)
92 on the hypotenuse of a right triangle is divided into two triangles and a high triangle similar to the original
93 Theorem 2 to determine the corresponding proportional sides and angles equal, two triangles are similar (SAS)
94 Theorem 3 to determine the corresponding three sides in proportion, the two triangles are similar (SSS)
95 Theorem If a right triangle's hypotenuse and a side angle of the hypotenuse of another right triangle

V: volume s: size a: long b: W h: high
; (1) surface area (length × width + height + length × width × height) × 2 S = 2 (ab + ah + bh)
(2) Volume = length × width × height V = abh
5, triangle
s area is a high end area = base × h high ÷ 2 s = ah ÷ 2
triangle = area × 2 ÷ high-end
; triangle = area × 2 ÷ at the end of high
6, parallelogram: s area of ​​a high-end area = base × h high s = ah
7, trapezoid: s area of ​​a base b on the lower end of h high area = (base + down on the bottom) × height ÷ 2 s = (a + b) × h ÷ 2
8 round: S C area perimeter Π d = diameter r = radius
(1) circumference = diameter × Π = 2 × Π × radius C = Πd = 2Πr
(2) area = radius × radius × Π
9, the cylinder: v volume h: s at the end of an area of ​​high underside of radius r c bottom perimeter
(1) side of the area = bottom circumference × height
(2) surface area = side area + base area × 2
(3) Volume = base area × height
(4) Volume = side area ÷ 2 × radius
10, cone: v s at the end of an area of ​​high volume h r the radius volume = base area × height ÷ 3

and fold problem
and ÷ (factor -1) = decimal
; decimal × multiplier = large numbers
(or and - decimals = large numbers)



48 Theorem quadrilateral angles and equal to 360 °
49 quadrilateral exterior angle equal to 360 °
50 n-sided polygon angles and theorems shape of the interior angles and equal to (n-2) × 180 °
51 deduction equal to any multilateral exterior angle and 360 °
52 parallelogram parallelogram nature of Theorem 1 is equal to the angular nature of
53 parallelogram parallelogram's Theorem 2 from the opposite side
54 inference caught in between two parallel lines, parallel line segments equal
55 parallelogram nature of Theorem 3 diagonal parallelogram line of a parallelogram bisect each other
56 Theorem 1 to determine the two groups were equal to the angle of the quadrilateral is a parallelogram
57 Parallelogram Theorem 2 to determine the two sides were equal to the quadrilateral is a parallelogram
58 Theorem 3 diagonal parallelogram bisect each other to determine the quadrilateral is parallelogram parallelogram
59 Theorem 4 to determine a set of parallel sides of the quadrilateral is a parallelogram equal
60 rectangular nature of the Theorem 1 the four corners of the rectangle are right angles
61 rectangular nature of the diagonal of the rectangle equal to Theorem 2
62 rectangles to determine the angle of Theorem 1 has three quadrilateral is a rectangle are right angles to determine the rectangle
63 Theorem 2 diagonal parallelogram is a rectangle of equal
64 diamond diamond nature of the Theorem 1 the four sides are equal
; 65 diamond diamond diagonal nature of Theorem 2 perpendicular to each other, and each diagonal split a diagonal
66 diamond-shaped area = half the product of the diagonal, ie S = (a × b) ÷ 2
67 diamond Theorem 1 to determine the four sides of the quadrilateral are equal is Diamond Diamond
68 Theorem 2 to determine the perpendicular diagonal parallelogram is a square nature of the diamond
69 Theorem 1 the four corners of a square are right angles, four sides are equal
70 square nature of the two diagonal square Theorem 2 are equal and mutually perpendicular bisector , each of

cut regular n-gon theorem of any regular polygon
138 has a circumcircle and an inscribed circle, two circles are concentric circles
139 regular n-gon of each interior angle is equal to (n-2) × 180 ° / n
140 Theorem regular n-gon of radius and apothem the regular n-gon is divided into two congruent triangles
2n ; 141 regular n-gon of area Sn = pnrn / 2 p for positive n-gon of perimeter
142 triangle area of ​​√ 3a / 4 a side said If long
143 around a vertex has k regular n-gon of angle, angle, and these should be 360 ​​°, so k ×

(n-2) 180 ° / n = 360 ° into the (n-2) (k-2) = 4 144 arc length formula: L = n Wu R/180
145 fan-shaped area of ​​the formula: S = n Wu R fan ^ 2 / 360 = LR / 2
146 common tangent length = d-(Rr) grandfather tangent length = d-(R + r)

utility: common mathematical formula

classification formula formula expression

12 +22 +32 +42 +52 +62 +72 +82 + ... + n2 = n (n +1) (2n +1) / 6 ;
1 * 2 +2 * 3 +3 * 4 +4 * 5 +5 * 6 +6 * 7 + ... + n (n + 1) = n (n +1) (n +2) / 3

sines a / sinA = b / sinB = c / sinC = 2R Note: where R represents the triangle's circumcircle radius
Cosine b2 = a2 + c2-2accosB Note: Angle B side a and side c is the angle between the

the standard equation of circle (xa) 2 + (yb) 2 = r2 Note: (a, b) is the circle center coordinates
general equation x2 + y2 + Dx + Ey + F = 0 Note: D2 + E2-4F> 0
standard parabolic equation y2 = 2px y2 =- 2px x2 = 2py x2 =- 2py
straight prism lateral area S = c * h oblique prism lateral area S = c '* h
; are pyramid lateral area S = 1/2c * h 'is bevel side of the area S = 1 / 2 (c + c') h '
round table side area S = 1 / 2 (c + c ') l = pi (R + r) l the ball surface area S = 4pi * r2
cylindrical side of the area S = c * h = 2pi * h tapered side of the area S = 1 / 2 * c * l = pi * r * l

arc length formula l = a * ra is the central angle of radians r> 0 fan-shaped area of ​​the formula s = 1 / 2 * l * r
cone volume formula V = 1 / 3 * S * H ​​cone volume formula V = 1 / 3 * pi * r2h
oblique prism volume V = S'L Note: one, S 'is a straight cross-sectional area, L is longer side edges
; cylinder volume formula V = s * h cylinder V = pi * r2h



1, square: C S perimeter area of ​​a side perimeter = side length × 4 C = 4a area = side × side length S = a × a
2, cube: V: Volume a: surface area = edge long edge long edge long × 6 S × = a table × a × 6

; (a + b) ÷ 2 S = L × h
83 (1) If the fundamental nature of the proportion a: b = c: d, then ad = bc if ad = bc, then a: b = c: d
84 (2) the nature of compliance than if a / b = c / d, then ( a ± b) / b = (c ± d) / d
85 (3) geometric properties if a / b = c / d = ... = m / n (b + d + ... + n ≠ 0), then (a + c + ... + m) /


split point connection tangent of the angle between the two outer
127 round cut on the side of the quadrilateral and the two groups are equal
Theorem Xianqie Jiao Xian Qiejiao it is equal to 128 arc of the circumference of the clip angle
129 deduction if the clip two Xianqie Jiao arc equal, then this is also equal to two Xianqie Jiao Theorem
130 intersect within the circle two chords intersect chord,Coach Audrey Collection, is divided into two segments intersection length equal to the product of inference if
131 and the diameter perpendicular to the string, then the string is half the diameter of it into two sub-segments


average


to catch problems
distance = speed chase and chase and the time difference ×
; chase and chase and time = distance ÷ speed difference = difference
speed chase and chase and distance ÷ time


÷ total number of shares =

RMB unit conversion
1 yuan = 10 jiao
; an angle = 10
1 dollar = 100 cents

what these two graphics on this point the nature of symmetry
74 isosceles trapezoid Theorem isosceles trapezoid on the bottom of the same two angles are equal
75 isosceles trapezoid of the two diagonals are equal
Theorem 76 to determine the isosceles trapezoid in the same two corners on the bottom of the trapezoid is isosceles trapezoid are equal
77 diagonal equal trapezoid is isosceles trapezoid
78 equal portions parallel segments Theorem If a group of parallel lines were cut in a straight line segments are equal, then


solute concentration problems


corresponding sides of a triangle with the original proportion
90 parallel to Theorem triangle and the other side of the line on both sides (or both sides of the extension cord) intersect, the structure

volume = length × edge long edge × edge length of V = a × a × a
3, rectangular
; C S perimeter area of ​​a side perimeter = (length + width) × 2 C = 2 (a + b) area = length × width S = ab
; 4, rectangular

hydrostatic speed + speed = flow rate
hydrostatic upstream speed = speed - flow rate
hydrostatic speed = (speed + upstream downstream speed) ÷ 2
flow rate = (downstream speed - upstream rate) ÷ 2

2, closed the line number of questions on the relationship between tree planting as
number of trees = number of segments = length = length ÷ spacing
spacing × number of trees
spacing = length ÷ number of trees


What symmetry axis at the intersection

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