Form 1441: Fill & Download for Free

There’s the Apollo retroreflectors.1441: Turnabout - explain xkcdA retrorefelctor is an array of mirrors that will bounce back a laser. The Apollo astronauts left some behind on the Moon so that astronomers on Earth could use them to measure the distance between the two bodies.And they have used them. Planetariums around the world make use of the retroreflectors every year. It is impossible for the retroreflectors to be there if we didn’t go to the moon. And any conspiracy to “fake the data” would have to involve literally every planetarium on Earth.That’s about as definitive as proof gets.

For simplicity let’s set[math][/math][math] [/math][math][/math][math] [/math][math][/math][math]\ [/math][math][/math][math]\ [/math][math][/math][math]\ [/math][math][/math][math]\ w=a+bi,\ [/math][math][/math][math]\ [/math][math][/math][math] w\in \C, [/math][math][/math][math]\ [/math][math][/math][math]\ a,b \in R[/math]Then we can go[math]w^{1441}=\overline {w} [/math][math][/math][math] \implies[/math][math][/math][math] [/math][math][/math][math]\| w^{1441}\|= [/math][math][/math][math]\| \overline {w} [/math][math][/math][math] [/math][math][/math][math]\| \iff[/math][math][/math][math] [/math][math][/math][math]\| w \|^{1441}= [/math][math][/math][math]\| {w} [/math][math][/math][math]\| \iff[/math][math][/math][math] [/math][math][/math][math]\| w \|^{1441}- [/math][math][/math][math]\| {w} \|=0 \iff[/math][math][/math][math] [/math][math][/math][math]\| {w} [/math][math][/math][math]\|(\| w \|^{1440}–1)=0 \iff[/math][math][/math][math] [/math][math][/math][math]\| {w} [/math][math][/math][math]\| =0 [/math][math][/math][math]\ [/math][math][/math][math]\ [/math][math][/math][math][/math]or [math][/math][math]\ [/math][math][/math][math]\ [/math][math][/math][math] [/math][math][/math][math]\| {w} \|=1 [/math][math][/math][math]\ [/math][math][/math][math]\ [/math][math][/math][math]\ [/math][math][/math][math]\ [/math][math][/math][math]( [/math][math][/math][math]\ [/math][math][/math][math]\ [/math][math][/math][math][/math]because[math][/math][math]\ [/math][math][/math][math]\ [/math][math][/math][math] [/math][math][/math][math]\| {w} \|\in \R_+)[/math]If [math][/math][math] [/math][math][/math][math]\| {w} [/math][math][/math][math]\| =0 [/math][math][/math][math][/math] then[math]\boxed {w =0 \implies [/math][math][/math][math] a=b=0} [/math][math][/math][math][/math]and if [math][/math][math] [/math][math][/math][math]\| {w} [/math][math][/math][math]\| =1 [/math][math][/math][math]\ [/math][math][/math][math]\ [/math][math][/math][math][/math] we get[math]w^{1441}=\overline {w} \implies[/math][math]w^{1441}\cdot w=\overline {w}\cdot w \implies[/math][math]w^{1442}=\| {w} \|^2 \implies[/math][math]w^{1442}=1 \implies[/math][math]w^{1442}=\cos 0 [/math][math][/math][math]+ i \sin 0 \implies [/math][math][/math][math][/math][math]w_{_k}=\cos \frac {2k\pi +0}{1442} [/math][math][/math][math]+ i \sin \frac{2k\pi+0}{1442} [/math][math][/math][math], [/math][math][/math][math]\ [/math][math][/math][math]\ [/math][math][/math][math] k\in [/math][math][/math][math]\{ 0,1,2, \ldots [/math][math][/math][math], [/math][math]1441[/math][math]\} \implies[/math][math]\boxed {w_{_k}=\cos \frac {k\pi }{721} [/math][math][/math][math]+ i \sin \frac{k\pi}{721} [/math][math][/math][math], [/math][math][/math][math]\ [/math][math][/math][math]\ k\in [/math][math][/math][math]\{ 0,1,2, \ldots [/math][math][/math][math], [/math][math]1441[/math][math]\}}[/math]or using the identity [math][/math][math]\ [/math][math][/math][math]\ [/math][math][/math][math]\ e^{i\theta}=\cos\theta+i\sin\theta[/math][math]w_{_k}=e^{\frac {2k\pi i }{1442}} \implies[/math][math]\boxed {w_{_k}=e^{\frac {k\pi i }{721}}, [/math][math][/math][math]\ [/math][math][/math][math]\ k\in [/math][math][/math][math]\{ 0,1,2, \ldots [/math][math][/math][math], [/math][math]1441[/math][math]\} [/math][math][/math][math] [/math][math][/math][math]}[/math]

The best source for this issue is John Ashdown-Hill’s biography of the Duchess of York entitled Cicely Neville: Mother of Richard III (2018). As only Ashdown-Hill can do, the author has tracked down various references to Edward’s birth, which were not consistently recorded by persons contemporary with the event, and makes a good case for his statement that Edward was conceived at Hatfield House in Hertfordshire May/June 1441 (by Cecily Neville and her husband, Richard, Duke of York) and born in Rouen, France, in February or March 1441/2. (See Chapter 3, “Cecily’s List of Children,” for an exhaustive explanation.)Of course, readers of Shakespeare’s play Richard III are well aware of the deception that the character, Richard, Duke of Gloucester, planned as part of his plot to usurp the throne, where he instructs Buckingham publicly to “infer the bastardy of Edward’s children,” adding:Nay, for a need, thus far come near my person:Tell them, when that my mother went with childOf that unsatiate Edward, noble YorkMy princely father then had wars in FranceAnd, by just computation of the time,Found that the issue was not his begot;Which well appeared in his lineaments,Being nothing like the noble duke my father:But touch this sparingly, as 'twere far off,Because you know, my lord, my mother lives. (III.5)However, of this, Ashdown-Hill writes, “There is no evidence for the claim which was put forward later (for example, by Vergil), to the effect that the sermons [by Dr. Shaw in London in 1483] focused on the bastardy myth in respect of Edward IV” (n. 36, p. 263).