R*o
发帖数: 3781 | 1 C. Full Exegetical Outline
Idea: All men, Jew and Gentile alike, are sinners and will not be declared r
ighteous, i.e., attain a right standing with God, through works of the law.
I. The Jews are no better off than the Gentiles because all alike under sin
(3:9).
II. There is no one who has any standing before God on their own, for there
is no one who is righteous, understands or seeks God, or shows kindness; tog
ether all have become worthless (3:10-12).
A. There is no one who is righteous (3:10... 阅读全帖 |
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R*o
发帖数: 3781 | 2 C. Full Exegetical Outline
Idea: The way in which God freely and graciously justifies any sinner, Jew o
r Gentile, as testified to in the Law and the Prophets, is not by works of t
he Law, but by faith in Christ's atoning sacrifice—a sacrifice which demons
trates God's justice in dealing with sin and at the same time excludes all h
uman boasting.
I. The way in which God freely and graciously justifies any sinner, Jew or G
entile, as testified to in the Law and the Prophets, is not by works of th... 阅读全帖 |
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R*o
发帖数: 3781 | 3 C. Full Exegetical Outline
Idea: The way in which God freely and graciously justifies any sinner, Jew o
r Gentile, as testified to in the Law and the Prophets, is not by works of t
he Law, but by faith in Christ's atoning sacrifice—a sacrifice which demons
trates God's justice in dealing with sin and at the same time excludes all h
uman boasting.
I. The way in which God freely and graciously justifies any sinner, Jew or G
entile, as testified to in the Law and the Prophets, is not by works of th... 阅读全帖 |
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R*o
发帖数: 3781 | 4 by Dave Hunt
Confronting A Vital Distinction
For the Calvinist to uphold his extreme view of control, God must be the cau
se of man's total depravity and the negative response it produces. There is
no way to escape this conclusion. If God were not the cause of man's sin, ma
n would be acting independently of God, and that cannot be allowed for anyth
ing in the Calvinist scheme. It follows, then, that "He [God] could ... have
prevented it [the fall and entrance of sin into the world], but He did ... 阅读全帖 |
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R*o
发帖数: 3781 | 5 B. Translation of Passage in NET
5:12 So then, just as sin entered the world through one man and death throug
h sin, and so death spread to all people because all sinned—
5:13 for before the law was given, sin was in the world, but there is no acc
ounting for sin when there is no law.
5:14 Yet death reigned from Adam until Moses even over those who did not sin
in the same way that Adam (who is a type of the coming one) transgressed.
5:15 But the gracious gift is not like the transgression. For i... 阅读全帖 |
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R*o
发帖数: 3781 | 6 6:14 Verse 14 rounds out the paragraph and gives the answer (which follows f
rom vv. 2-11) to the initial question posed in v. 1. The for (gavr, gar) whi
ch begins the verse links it closely with the preceding verses and indeed th
e question of the passage as a whole: “Should the Christian under grace con
tinue to sin?” Answer: “No, because we were placed under grace in order th
at sin may longer reign over us.”
While the overall sense of 6:14 in its context is clear, the two principle c
lauses ... 阅读全帖 |
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z********o
发帖数: 18304 | 7 版上有同学转了个新闻：一对基督徒夫妇，孩子生病了，不送孩子看医生，两个孩子都
不幸亡故。
下面是那对基督徒夫妇的教会的一篇布道：
http://www.fcgchurch.org/Messages/Pages/Healing%20-%20from%20Go
Healing - From God or Medicine?
Since God cannot change; Jesus is the same; and the Holy Spirit
is with us, then the same healing all through the Bible, is the healing from
God anyone can receive who believes. The healing ministry of Jesus is all
through the New Testament, and since He is Hebrews 13:8 “the same yesterday
, and to day, and for ever,” then w... 阅读全帖 |
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J*******g
发帖数: 8775 | 8 这个问题我自己都回答了至少两遍了。
你对这段经文理解有问题。
这段是说信耶稣应该是如重生一般，真正信主的人要认识自己的罪，而避免延续之前的
恶的行为。信主的人身上会看到行为向好的方向的变化。
但不排除基督徒犯错。请看，在你引的经文前两章：
1 John 1
8 If we claim to be without sin, we deceive ourselves and the truth is not
in us. 9 If we confess our sins, he is faithful and just and will forgive us
our sins and purify us from all unrighteousness. 10 If we claim we have not
sinned, we make him out to be a liar and his word is not in us.
1 John 3:
8 The one who does what is sinful is of the devil, because the devil ... 阅读全帖 |
|
发帖数: 1 | 9 88 Bible Verses about
Harsh Words
Proverbs 15:1 ESV / 213 helpful votes Helpful Not Helpful
A soft answer turns away wrath, but a harsh word stirs up anger.
Ephesians 4:29 ESV / 122 helpful votes
Let no corrupting talk come out of your mouths, but only such as is good for
building up, as fits the occasion, that it may give grace to those who hear.
Proverbs 29:11 ESV / 111 helpful votes
A fool gives full vent to his spirit, but a wise man quietly holds it back.
James 1:19-20 ESV / 92 h... 阅读全帖 |
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h*******e
发帖数: 1968 | 10 粗略推了一下，
Trr=Txx cos^2+ Tyy sin^2 + (Txy+Tyx)sin cos
T@@=Txx sin^2+ Tyy cos^2 - (Txy+Tyx)sin cos
Tr@=(-Txx+Tyy)sin cos + Txy cos^2-Tyx sin^2
T@r=(-Txx+Tyy)sin cos - Txy sin^2+Tyx cos^2
不知道是不是所有符号都正确了，能有书确定一下就好了 |
|
w**********y
发帖数: 1691 | 11 You are still confused...
First, definition of martingale is: E(X_t|F_s)=X_s, s
So you need to prove E[sin(W_t)-sin(W_s)|F_s]=0. Following your ito formula,
sin(W_t)-sin(W_s) = \int_{s}^{t}cos(W_u)dW_u - 1/2\int_{s}^{t}sin(W_u)du
The first term is ito integrals, whose expectation AND ALSO conditional
expectation is zero;
As for the second term, E(\int_{s}^{t}sin(W_u)du)=0, BUT!!! E(\int_{s}^{t}
sin(W_u)du|F_s) \neq 0 (should be s*sin(W_s)?? need check.).
If you don't understa... 阅读全帖 |
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D**u
发帖数: 204 | 12 The law of sin in R^3 is different from the plane case.
In R^3, the law of sin is instead to be:
sin(a)/sin(alpha) = sin(b)/sin(beta) = sin(c)/sin(gamma),
where alpha, beta and gamma are the dihedral angles
between the vectors. |
|
s***e
发帖数: 911 | 13
经度和纬度的定义我不知道, 不过猜测估计是球坐标下的两个角度:
定义两级连线的一个方向为z方向, 纬度是坐标位置矢量和z轴夹角,
设为\theta(坐标原点取为地球心); 设和z轴垂直的任何一个方向为x轴,
选x-z平面的法线为y轴. 则经度应当是位置坐标在x-y平面投影线和x轴
的夹角,设为\phi. 设地球是个圆球,则地面任何一点坐标可以被经度和
纬度确定:
x0=R*Sin[\theta0]*Cos[\phi0]
y0=R*Sin[\theta0]*Sin[\phi0]
z0=R*Cos[\theta0]
另外一点坐标是:
x1=R*Sin[\theta1]*Cos[\phi1]
y1=R*Sin[\theta1]*Sin[\phi1]
z1=R*Cos[\theta1]
两个位置矢量之夹角\psi可以被算出:
x0*x1+y0*y1+z0*z1=R^2*Cos[\psi]
Cos[\psi]=Cos[\theta0]*Cos[\theta1]+Cos[\phi1-\phi0]*Sin[\theta0]*Sin[\tehta1]
经度纬度差肯定不能唯一确定一个距离的, 你得至少 |
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w**j
发帖数: 1032 | 14 The act of murder is rampant in the Bible. In much of the Bible,
especially the Old Testament, there are laws that command that people be
killed for absurd reasons such as working on the Sabbath, being gay, cursing
your parents, or not being a virgin on your wedding night. In addition to
these crazy and immoral laws, there are plenty of examples of God's
irrationality by his direct killing of many people for reasons that defy any
rational explanation such as killing children who make fun of... 阅读全帖 |
|
O*******d
发帖数: 20343 | 15 如果你会写C程序， 下边的算法给出的结果是一个定值1.5，不管t是什么值。
sin(0.0 + t) * sin (0.0 + t) + sin(2.0 / 3.0 * PI ＋ t) * sin(2.0 / 3.0 * PI
＋ t) + sin(1.0 / 3.0 * PI + PI + t) * sin(1.0 / 3.0 * PI + PI + t)
sin是正弦函数。 t是时间，可以是任意值。 PI是圆周率3.14159...
就是说，三个峰值一样的，相差120度的正弦波的平方之和，是一个常数。 这就是为什
么三相发电机
的输出功率是不随时间脉动的原因。 |
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a*o
发帖数: 25262 | 16 帮你找个证明吧， n = 2.
For any positive integers n and x in (0,1) we can define
2n
x^n (1 - x)
^n 1 --- j
f(x) = ---------------- = ---- ) c_j x
n! n! ---
j=n
Here, c_j are integers. For x in (0,1) we have,
0 < f(x) < 1/n!
Now, suppose that positive integers a and b exist such that
2 a
pi = ---
b
Define
n / 2n 2n-2 ... 阅读全帖 |
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G*M
发帖数: 6042 | 17 Bible Course - Christian Doctrine
Lesson 4
God the Father
Lord's Days 8 - 10
God the Father
A true Christian may be aware of comfort for himself, now and in the future,
when in possession of the favor of God. This blessedness is in the hands of
a triune God. The knowledge of a triune God is indispensable for salvation.
This lesson speaks of the Trinity in general and of God the Father in
particular.
Lord's Day 8
Q. 24. How are these articles divided?
A. Into three parts; the first is of God the ... 阅读全帖 |
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S*********L
发帖数: 5785 | 18 我多次遇到这个问题，也就是一个词对多义的问题。
我的具体处理：如果上下文不清楚，则SIN=罪性和罪行。如果说的是本性SIN=罪性；如
果说的有罪的言行SIN=罪行。一般英文也不是一成不变地用SIN，而是根据情况，用
SINFUL NATURE， SINFUL DEEDS，或者ORIGINAL SIN 等等。
不过不管哪种用法，都需要更多了解相关的语境。 |
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C****i
发帖数: 1776 | 19 CHAPTER 5
OF PROVIDENCE
1. God the great Creator of all things doth uphold, direct, dispose, and gov
ern all creatures, actions, and things, from the greatest even to the least,
by his most wise and holy providence, according to his infallible foreknowl
edge, and the free and immutable counsel of his own will, to the praise of t
he glory of his wisdom, power, justice, goodness, and mercy.
2. Although, in relation to the foreknowledge and decree of God, the first C
ause, all things come to pass i... 阅读全帖 |
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R*o
发帖数: 3781 | 20 We can begin to see how a confusion of person and nature leads to a very lim
ited God with no free choice. . . .
. . . . of vital importance to the discussion on Total depravity, and unfor
tunately all but neglected by most Reformed in my experience, is the doctrin
e of the incarnation. This brings the discussion of human nature out of the
simply anthropological realm and into the christological realm.
The crux of the matter is this: if Christ did not have a human nature, then
He cannot save u... 阅读全帖 |
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C****i
发帖数: 1776 | 21 59. 什么是“双重预定”？圣经这样教导吗？
What is “double predestination,” and does the bible teach it?
诚之获授权翻译。
原文载于：http://www.monergism.com/thethreshold/articles/onsite/qna/double.h
tml
“双重预定”的意思只是说，正如神预定了一些而不是所有的人，使他们得到永恒的救
恩，因此，祂也预定其他人受永恒的刑罚；“双重”预定这第二部分，即上帝派定所有
未蒙拣选的，要遭受永恒的灭亡，有时候也被称为“遗弃”（reprobation）；因此，那
些非选民就被称为“弃民”（reprobate）。从逻辑上说，如果下面的前提可以成立，那
么，遗弃的教义必然是真的：1) 上帝主权地拣选了一些人得救；2) 上帝没有拣选所有
的人得救；3) 除了上帝主权的拣选之外，人不可能得到救恩。换句话说，如果上帝无误
地选择要救一些人，也断绝其他人得救的任何其他方式，祂就实际上对所有曾经活着的
人做了选择：祂要不是选择救这个人，就是断绝任何使他得救的盼望。所有这些前提当
然都... 阅读全帖 |
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C****i
发帖数: 1776 | 22 CHAPTER XXI
Of Religious Worship, and the Sabbath Day
I. The light of nature showeth that there is a God, who hath lordship and so
vereignty over all, is good, and doth good unto all, and is therefore to be
feared, loved, praised, called upon, trusted in, and served, with all the he
art, and with all the soul, and with all the might.[404] But the acceptable
way of worshiping the true God is instituted by himself, and so limited by h
is own revealed will, that he may not be worshiped according to... 阅读全帖 |
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l**********t
发帖数: 5754 | 23 chapter 9.1 The Flesh And Man’s Breakdown
Romans 7 has a new lesson to teach us. It is found in the discovery that I
am “in the flesh” (Rom. 7:5), that “I am carnal” (7:18). This goes
beyond the question of sin, for it relates also the matter of pleasing God.
We are dealing here not with sin in its forms but with man in his carnal
state. The latter includes the former but it takes us a stage further, for
it leads to the discovery that in this realm too we are totally impotent,
and that “they tha... 阅读全帖 |
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l**********t
发帖数: 5754 | 24 chapter 10.5 The Fourth Step: “Walk... After The Spirit”
“For what the law could not do, in that it was weak through the flesh,
God,
sending his own Son in the likeness of sinful flesh and as an offering
for
sin, condemned sin in the flesh: that the ordinance of the law might be
fulfilled in us, who walk not after the flesh, but after the Spirit”
(Rom.
8:3).
Every careful reader of these two verses will see that there are two
things
presented here. They are, firstly, what the Lord Jesus has done... 阅读全帖 |
|
l**********t
发帖数: 5754 | 25 chapter 9.1 The Flesh And Man’s Breakdown
Romans 7 has a new lesson to teach us. It is found in the discovery that I
am “in the flesh” (Rom. 7:5), that “I am carnal” (7:18). This goes
beyond the question of sin, for it relates also the matter of pleasing God.
We are dealing here not with sin in its forms but with man in his carnal
state. The latter includes the former but it takes us a stage further, for
it leads to the discovery that in this realm too we are totally impotent,
and that “they tha... 阅读全帖 |
|
l**********t
发帖数: 5754 | 26 chapter 10.5 The Fourth Step: “Walk... After The Spirit”
“For what the law could not do, in that it was weak through the flesh,
God,
sending his own Son in the likeness of sinful flesh and as an offering
for
sin, condemned sin in the flesh: that the ordinance of the law might be
fulfilled in us, who walk not after the flesh, but after the Spirit”
(Rom.
8:3).
Every careful reader of these two verses will see that there are two
things
presented here. They are, firstly, what the Lord Jesus has done... 阅读全帖 |
|
C****i
发帖数: 1776 | 27 CHAPTER XXVIII
Of Baptism
I. Baptism is a sacrament of the new testament, ordained by Jesus Christ,[52
2] not only for the solemn admission of the party baptized into the visible
church;[523] but also, to be unto him a sign and seal of the covenant of gra
ce,[524] of his ingrafting into Christ,[525] of regeneration,[526] of remiss
ion of sins,[527] and of his giving up unto God, through Jesus Christ, to wa
lk in newness of life.[528] Which sacrament is, by Christ’s own appointment
, to be contin... 阅读全帖 |
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C****i
发帖数: 1776 | 28 CHAPTER XXVIII
Of Baptism
I. Baptism is a sacrament of the new testament, ordained by Jesus Christ,[52
2] not only for the solemn admission of the party baptized into the visible
church;[523] but also, to be unto him a sign and seal of the covenant of gra
ce,[524] of his ingrafting into Christ,[525] of regeneration,[526] of remiss
ion of sins,[527] and of his giving up unto God, through Jesus Christ, to wa
lk in newness of life.[528] Which sacrament is, by Christ’s own appointment
, to be contin... 阅读全帖 |
|
R*o
发帖数: 3781 | 29 1:28 Continuing on, Paul says that just as people did not see fit to acknowl
edge God, he gave them over to a depraved mind, to do things that are not fi
tting. The expression to see fit to acknowledge God is literally “they did
not approve to have God in [their] knowledge.” The word approve (ejdokivmas
an, edokimasan) means “to test,” “to examine,” “to come to a conclusion
based on evidence.” And the idea of knowledge (ejpignwvsi", epignosis) alw
ays means “moral or religious knowledge” in the ... 阅读全帖 |
|
R*o
发帖数: 3781 | 30 1:28 Continuing on, Paul says that just as people did not see fit to acknowl
edge God, he gave them over to a depraved mind, to do things that are not fi
tting. The expression to see fit to acknowledge God is literally “they did
not approve to have God in [their] knowledge.” The word approve (ejdokivmas
an, edokimasan) means “to test,” “to examine,” “to come to a conclusion
based on evidence.” And the idea of knowledge (ejpignwvsi", epignosis) alw
ays means “moral or religious knowledge” in the ... 阅读全帖 |
|
R*o
发帖数: 3781 | 31 4:15 In 4:15 Paul gives another reason why Abraham and his descendents will
not become heirs by obedience to the law. It is because the law brings wrath
(oJ gaVr novmo" ojrghVn katergavzetai, ho gar nomos orgen katergazetai). Th
e only thing the law can do is to reveal sin. It cannot help a person overco
me sin and thus avoid the wrath of God.
Paul makes it clear that the law of God incites the wrath of God. But he con
tinues on in this verse to say that where there is no law, there is no trans
... 阅读全帖 |
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R*o
发帖数: 3781 | 32 How can there be any real freedom of choice if only one kind of choice is av
ailable, and one which has been decreed eternally? But would a Holy God decr
ee evil? Obviously, this is not free choice at all. It is, however, the only
"freedom" Calvinism can allow. Pink favorably quotes J. Denham Smith, whom
he honors as a "deeply taught servant of God":
I believe in free will; but then it is a will only free to act according to
nature . . .. The sinner in his sinful nature could never have a will a... 阅读全帖 |
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R*o
发帖数: 3781 | 33 B. Translation of Passage in NET
6:15 What then? Shall we sin because we are not under law but under grace? A
bsolutely not!
6:16 Do you not know that if you present yourselves as obedient slaves, you
are slaves to the one you obey, either to sin resulting in death, or obedien
ce resulting in righteousness?
6:17 But thanks be to God that though you were slaves to sin, you obeyed fro
m the heart that pattern of teaching you were entrusted to,
6:18 and having been freed from sin, you became enslav... 阅读全帖 |
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C*****e
发帖数: 367 | 34 【 以下文字转载自 Church 俱乐部 】
发信人: CCBible (神同在圣经), 信区: Church
标 题: 海德堡要理问答主日30
发信站: BBS 未名空间站 (Mon Apr 23 01:29:01 2012, 美东)
海德堡要理问答主日30
来自基督徒百科
目录
1 英文版
2 英文2011版
3 赵中辉版
4 陈达/王志勇版
5 基督教要义圣经课程版
6 链接参考
英文版
30. Lord's Day
Q. 80.
What difference is there between the Lord's supper and the popish mass?
A.
The Lord's supper testifies to us, that we have a full pardon of all sin by
the only sacrifice of Jesus Christ, which he himself has once accomplished o
n the cross; (a)
and, that we by the Holy Ghost ar... 阅读全帖 |
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E*V
发帖数: 200 | 35 First the bad news.
Because we have sinned we are born separated from God. Without intervention
, we are ineligible for Heaven. This applies to the entire human race. You
are not alone.
Romans 3:23 says, "For all have sinned, and come short of the glory of God;"
Romans 3:10 says, "As it is written, There is none righteous, no, not one:"
Romans 6:23a "For the wages of sin is death;"
Revelation 21:8 "But the fearful, and unbelieving, and the abominable, and m
urderers, and whoremongers, and sor... 阅读全帖 |
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B*********e
发帖数: 254 | 36 Bible Research > Textual Criticism > Story of the Adulteress
Concerning the Story of the Adulteress
in the Eighth Chapter of John
Biblical scholars are nearly all agreed that the Story of the Adulteress (al
so known as the Pericope Adulterae or the Pericope de Adultera) usually prin
ted in Bibles as John 7:53-8:11 is a later addition to the Gospel. On this p
age I present some extended quotations from scholarly works that explain the
reasons for this judgment. On another page I give an extract f... 阅读全帖 |
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B*********e
发帖数: 254 | 37 A Sermon on the Pericope Adulterae
Bible Research > Textual Criticism > Story Of The Adulteress > Quo Vadis?
Quo Vadis?
A Sermon on the Pericope Adulterae
by Michael Marlowe, 2004
The Quo Vadis story is one of those Legends of the Saints that are well-know
n to Catholics but practically unknown to Protestants. It is an ancient lege
nd concerning Peter's martyrdom, believed to be from the second century, and
preserved in the collection of legends included in the apocryphal Acts of P
eter. George ... 阅读全帖 |
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T*****n
发帖数: 2456 | 38 我老人家摘录的 DECLARATION一些核心部分：
3. The Common Understanding of Justification
14.The Lutheran churches and the Roman Catholic Church have together
listened to the good news proclaimed in Holy Scripture. This common
listening, together with the theological conversations of recent years, has
led to a shared understanding of justification. This encompasses a consensus
in the basic truths; the differing explications in particular statements
are compatible with it.
15.In faith we together hold the convicti... 阅读全帖 |
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h**********c
发帖数: 4120 | 39 先前提到过 y = sin(a * pi /x), 对于质数a 在（1，a）是没有解得。
写了段程序，用牛顿法算 x， 跑了跑发现，原来这个一维系统有很多folds，又想了想
能不能用二维的系统来解这个问题呢？于是又了如下的构造
f = (f1,f2)^t
f1(x1,x2) = (x1 + exp(x2))* sin(pi * a /x1);
f2(x1,x2) = (x1*x1 -x2*x2)
求 f --〉0
这个系统看起来有个不错的jacobian，跑了跑程序，居然收敛了，但不知道收敛到哪里
去了，您有时间帮忙看看吧，能不能有更好的构造。或者用什么论证着干脆就是不可行
的，免得骑自行车去月球。
附程序c++
#include
#include
using namespace std;
#define PI (atan(1.0)*4.0)
#define __VERYSMALL (1.0E-10)
#define __ITERATIONLIMIT 20
bool isVerySmall (double d) {
return (a... 阅读全帖 |
|
w****o
发帖数: 20 | 40 My Mathematica shows that:
Integrate[Exp[-x^2]*Sin[x^2]/x^2,{x,-Infinity,
Infinity}]=2^(5/4)*Pi^(1/2)*Sin[Pi/8]=1.613;
Integrate[Exp[-x^2]*Sin[x]^2/x^2,{x,-Infinity,
Infinity}]=Sqrt[Pi]*(-1+1/e+Sqrt[Pi]*Erf[1])=1.527;
I think you can do your integral analytically (integration by parts):
Exp[-x^2]*Sin[x]^2/x^2 dx
=-Exp[-x^2]*Sin[x]^2 d(1/x)
=...
Finally you can reduce the integrand into a linear combination of
Integrate[Exp[-x^2]*Sin[x]/x] and Integrate[Exp[-x^2]*Sin[x]], which you all
know how t |
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h**********c
发帖数: 4120 | 41 先前提到过 y = sin(a * pi /x), 对于质数a 在（1，a）是没有解得。
写了段程序，用牛顿法算 x， 跑了跑发现，原来这个一维系统有很多folds，又想了想
能不能用二维的系统来解这个问题呢？于是又了如下的构造
f = (f1,f2)^t
f1(x1,x2) = (x1 + exp(x2))* sin(pi * a /x1);
f2(x1,x2) = (x1*x1 -x2*x2)
求 f --〉0
这个系统看起来有个不错的jacobian，跑了跑程序，居然收敛了，但不知道收敛到哪里
去了，您有时间帮忙看看吧，能不能有更好的构造。或者用什么论证着干脆就是不可行
的，免得骑自行车去月球。
附程序c++
#include
#include
using namespace std;
#define PI (atan(1.0)*4.0)
#define __VERYSMALL (1.0E-10)
#define __ITERATIONLIMIT 20
bool isVerySmall (double d) {
return (a... 阅读全帖 |
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s*****c
发帖数: 753 | 42 First, you have to make sure |x|+|y|的最小值 is what you want, and you don't
want x^2+y^2的最小值.
If you do need "the slope that gives you the minimal distance sum", then:
For your two points P1(x1, y1), P2(x2, y2)
convert to polar coordinate system.
P1: (r1, t1), P2: (r2, t2)
where
x1=r1*cos(t1), y1=r1*sin(t1), x2=r2*cos(t2), y2=r2*sin(t2).
从原点到P1的线和从原点到P2的线有个夹角。范围从0到180.
如果夹角小于90， 你要的直线必定是两者之间。
let t2>t1, and t2-t1<90degrees
for the straight line you want y=k*x, or x=r*cos(t), y=r*sin(t). t1
I... 阅读全帖 |
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g****t
发帖数: 31659 | 43 因为不是点到直线的y方向距离和最小，所以在课本上不是很常见。
GooG: absolute least square
First, you have to make sure |x|+|y|的最小值 is what you want, and you don't
want x^2+y^2的最小值.
If you do need "the slope that gives you the minimal distance sum", then:
For your two points P1(x1, y1), P2(x2, y2)
convert to polar coordinate system.
P1: (r1, t1), P2: (r2, t2)
where
x1=r1*cos(t1), y1=r1*sin(t1), x2=r2*cos(t2), y2=r2*sin(t2).
从原点到P1的线和从原点到P2的线有个夹角。范围从0到180.
如果夹角小于90， 你要的直线必定是两者之间。
let t2>t1, and t2-t1<90degrees
for the straig... 阅读全帖 |
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z****i
发帖数: 406 | 44 We have a+b+c = pi.
sin(c) = sin(pi-a-b) = sin(a+b) = sin(a) cos(b) + sin(b)cos(a) <= sin(a) +
sin(b) |
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s***e
发帖数: 911 | 45
指定一个方向作为园面的法向n, 你就指定了一个给定半径的园(下面设为a).
再指定圆面上两个正交矢量 k1, k2, 连同n就有了一个正交标架. 园方程就是:
r=a*(Cos[t] k1+Sin[t] k2)
t是参数,从0到Pi.
余下的问题就是通过给定的方向n(\theta,\phi)定出方向k1,k2. (\theta,\phi)是
通常球坐标方向角.
下面是一组满足上面条件的标架:
k=(Sin[\theta] Cos[\phi], (Sin[\theta] Sin[\phi], Cos[\theta])
k1=(-Sin[\phi], Cos[\Phi],0)
k2=(-Cos[\theta] Cos[\phi], -Cos[\theta] Sin[\phi], Sin[\theta]).
所以空间中给定半径的任意圆依赖于两个参数---两个方向角. |
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w*********g
发帖数: 30882 | 46
Rev. 12:1-5
Now a great sign appeared in heaven: a woman clothed with the sun, with the
moon under her feet, and on her head a garland of twelve stars. Then being
with child, she cried out in labor and in pain to give birth. And another
sign appeared in heaven: behold, a great, fiery red dragon having seven
heads and ten horns, and seven diadems on his heads. His tail drew a third
of the stars of heaven and threw them to the earth. And the dragon stood
before the woman who was ready to give bir... 阅读全帖 |
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t***h
发帖数: 5601 | 47 以D为原点, BC为实轴建立坐标系, 设 A=a+bi, B=c, C=-c
向量CA=a+c+bi, 向量BA=a-c+bi, 设 \theta = 角ABE = 角ACF
向量CF = (a+c+bi)*e^{-i\theta}*\cos\theta
向量BE = (a-c+bi)*e^{i\theta}*\cos\theta
F = (a+c+bi)*e^{-i\theta}*\cos\theta - c
= [a\cos^2\theta + b\sin\theta\cos\theta - c\sin^2\theta] +
[b\cos^2\theta - (a+c)\sin\theta\cos\theta] i
E = (a-c+bi)*e^{i\theta}*cos\theta + c
= [a\cos^2\theta - b\sin\theta\cos\theta + c\sin^2\theta] +
[b\cos^2\theta + (a-c)\sin\theta\cos\theta] i
展开计算可得 |F|^2 = |E|^2 |
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h******n
发帖数: 3599 | 48 非常精彩啊
http://www.cnn.com/2014/11/26/justice/ferguson-grand-jury-react
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l****z
发帖数: 29846 | 49 By Mark Rogers 12/28/2013 ·
This statement from GLAAD, a collection of gay and lesbian members:
“Phil Robertson should look African American and gay people in the eyes and
hear about the hurtful impact of praising Jim Crow laws and comparing gay
people to terrorists. If dialogue with Phil is not part of next steps then A
&E has chosen profits over African American and gay people – especially its
employees and viewers.”
The utter nonsense of that statement accusing Robertson of comparing gay
peop... 阅读全帖 |
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h******n
发帖数: 3599 | 50 【 以下文字转载自 Military 讨论区 】
发信人: hutuxian (糊涂仙), 信区: Military
标 题: CNN 终于可以comments了，一边倒的评价啊
发信站: BBS 未名空间站 (Wed Nov 26 16:20:17 2014, 美东)
非常精彩啊
http://www.cnn.com/2014/11/26/justice/ferguson-grand-jury-react
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