842 P.2d 596 (1992)
Earl SAM, Appellant,
v.
STATE of Alaska, Appellee.
No. A-4041.
Court of Appeals of Alaska.
November 27, 1992.
Andrew Haas, Asst. Public Defender, Bethel, and John B. Salemi, Public Defender, Anchorage, for appellant.
W.H. Hawley, Asst. Atty. Gen., Office of Sp. Prosecutions and Appeals, Anchorage, and Charles E. Cole, Atty. Gen., Juneau, for appellee.
Before BRYNER, C.J., and COATS and MANNHEIMER, JJ.
OPINION
BRYNER, Chief Judge.
Earl K. Sam was convicted by a jury of one count attempted murder in the first degree. AS 11.41.100(a)(1); AS 11.31.100. Superior Court Judge Richard D. Savell sentenced Sam to a term of forty-five years with fifteen years suspended. Sam appeals his conviction, arguing that the trial court erred in refusing to preclude the state from presenting expert testimony concerning Sam's capacity to form specific intent, in refusing to give Sam's proposed instructions dealing with attempt, in permitting the prosecutor to argue facts not in evidence, and in limiting Sam's final argument. Sam also argues that his sentence is excessive. We affirm.
Facts
In the early morning hours of July 24, 1989, J.E. was shot in the back of the head while walking in Akiachak. He managed to make his way to a nearby home, where he received assistance. The Alaska State Troopers were summoned to Akiachak from Bethel to investigate the shooting. They contacted various people, including Sam. When Trooper Robert Baty first spoke with Sam, Sam acknowledged that he had been waiting for the troopers to come; he also admitted he had been carrying a gun earlier that morning.
Trooper Warren Tanner then conducted a tape-recorded interview with Sam, who was cooperative, but "elusive," according to Tanner. In the course of the recorded interview, Sam evidently made a number of statements that were exculpatory. After completing the recorded interview, Sam agreed to show the troopers his gun, which he had hidden in an old fuel truck. The gun, a .12 gauge pump shotgun, was unloaded. Sam also led the troopers to the location where J.E. had been standing when he was shot. Nearby, in an area where the grass was matted, the troopers found a spent shotgun shell. Sam admitted that he had shot a person from this area.
Denial of Protective Order
After being indicted for attempted first-degree murder, Sam filed a motion, through counsel, for a psychiatric evaluation to determine his competency to proceed. He also served notice, pursuant to AS 12.47.020(a), of his intent to raise a defense of diminished capacity. After having been examined as an outpatient, Sam requested and received an order of commitment to the Alaska Psychiatric Institute (API) for further evaluation to determine his competency to proceed.
The state subsequently sought an order directing all experts who had examined Sam to supplement their competency evaluations by indicating whether they believed Sam had the capacity to form specific intent to kill. As support for its request, the state cited AS 12.47.070(c)(5), which specifies that if a mental examination is ordered to determine the competency of a person who has given notice of intent to rely on a defense of diminished capacity, the person performing the examination must report not only on the issue of competency, but also on the defendant's capacity to form the culpable mental state for the offense charged. Sam eventually indicated that he did not oppose the state's request.
Shortly before trial, however, Sam moved for a protective order, seeking to preclude the state from calling Dr. Criswell as an expert witness on the issue of diminished capacity. Criswell, a staff member at API, had examined Sam for purposes of determining his competency to proceed and had concluded not only that Sam was competent, but also that he was capable of forming specific intent to kill. In moving to suppress, Sam argued, among other things, that Criswell's testimony on diminished capacity should be excluded because Criswell had failed to record his examination of Sam. According to Sam, under Houston v. State, 602 P.2d 784, 796 (Alaska 1979), Criswell should have been required to record the examination.
The trial court denied Sam's motion for a protective order, ruling that Criswell could testify for the state if Sam elected to present expert testimony in support of a diminished capacity defense. Sam later abandoned his plan to raise diminished capacity, claiming, for the record, that his decision to do so was the result of the trial court's denial of his motion for a protective order. Criswell never testified.
On appeal, Sam attempts to resurrect his claim that Criswell's testimony should have been barred due to his failure to record the psychiatric examination. In our view, however, the Alaska Supreme Court's decision in State v. Wickham, 796 P.2d 1354, 1355-59 (Alaska 1990), mandates the conclusion that Sam's abandonment of his diminished capacity defense bars him from raising this issue on appeal.
In Wickham, the court, relying on Luce v. United States, 469 U.S. 38, 105 S.Ct. 460, 83 L.Ed.2d 443 (1984), declared that a defendant who declines to testify after receiving an unfavorable ruling on the admissibility of prior convictions for impeachment purposes will be deemed to have abandoned any resulting claim of error. The Wickham court concluded that meaningful appellate review is impeded in such situations by the uncertainty attendant to determining whether any error might ultimately have proven harmless. Wickham, 796 P.2d at 1358-59.
Sam argues that Wickham is distinguishable because it deals with a purely evidentiary issue a nonconstitutional claim that is subject to a relatively broad harmless error standard. In Sam's view, because his motion for a protective order was based on constitutional grounds and thus implicated a narrower standard of harmless error, there is considerably less room for uncertainty.
We are unpersuaded by this argument. The uncertainty that the supreme court spoke of in Wickham is essentially unrelated to the standard by which harmless error is measured in a given case. Wickham addressed the inherent uncertainty and artificiality of applying a harmless error analysis in a purely hypothetical or abstract context, a problem that is largely unaffected by the applicable harmless error standard.[1]
Given the core concern of Wickham, we believe that the circumstances of the present case militate even more strongly against appellate review than did the circumstances in Wickham. In Wickham, the defendant disclosed his proposed testimony in a clear and detailed offer of proof, which the trial court found acceptable; the state, for its part, unequivocally announced its intent to offer the prior convictions in evidence if the defendant testified; finally, the precise nature of the impeachment evidence was known, and its likely impact on the defendant's credibility was thus readily predictable. All of these circumstances added considerable certainty to the situation in Wickham. The supreme court nevertheless found appellate review undesirable.
In the present case, by contrast, Sam failed to provide the trial court with a detailed offer concerning his proposed defense of diminished capacity. Sam also failed to offer proof, or to request that the state make an offer, as to the specific testimony Criswell was likely to give in support of his conclusion that Sam was capable of forming specific intent. Furthermore, at no point did the prosecution unequivocally commit itself to calling Criswell as a rebuttal witness.
Any attempt to divine the likely effect of the alleged error in these circumstances would amount to pure speculation. For this reason, we hold that Sam's abandonment of his diminished capacity defense precludes review of the trial court's decision to allow Criswell to testify.
Sam's Proposed Instructions
Sam next claims that the trial court erred in refusing two proposed instructions on attempt. The first read as follows:
In order for a defendant to be convicted of attempted murder in the first degree, the district attorney must prove beyond a reasonable doubt that [the defendant was] really trying to kill the person when he shot him.
Even if you believe that the defendant shot him, we cannot automatically say that he was trying to kill him too. Perhaps there are other reasons the shooting happened. The district attorney must prove beyond a reasonable doubt that the defendant was trying to kill the person if and when he shot him.
Sam's second proposed instruction read as follows:
To convict a person of attempted murder in the first degree, the district attorney must prove beyond a reasonable doubt that the person made a plan to kill someone. Then, they must also prove that after making the plan, he tried to carry it out and tried to kill someone. They must show that he did this on purpose, to make his plan come true.
On appeal, Sam has simply argued that his proposed instructions embodied correct statements of the law. He has not demonstrated any error or incompleteness in the instructions that the jury actually received, nor has he shown how his proposed instructions were better or more accurate, or how they would have been of substantial assistance to the jury. As the trial court correctly found, the instructions on attempt and culpable mental state that were actually given to Sam's jury fully and accurately stated the applicable law, thereby addressing the concerns dealt with in Sam's proposed instructions. Under the circumstances, even assuming Sam's proposed instructions were unobjectionable, the trial court did not abuse its discretion in rejecting them. See Stoneking v. State, 800 P.2d 949 (Alaska App. 1990).
Prosecutor's Final Argument
Sam further claims that the trial court erred in allowing the prosecutor to argue facts not in evidence. During Sam's trial, Trooper Tanner testified that the distance from the matted area where Sam stood at the time of the shooting to the closest point on a nearby walkway was twenty-one feet, six inches, and that, at a right angle from this point, the distance up the walkway to the point at which J.E. was apparently shot measured fourteen feet, six inches. When the prosecutor asked Tanner to calculate the direct distance between Sam and J.E. from these measurements, however, Tanner evidently could not. The jury heard no testimony concerning the direct distance.
Nevertheless, during final argument, the prosecutor, who had calculated the distance by use of the Pythagorean theorem,[2] informed the jury that, based on Tanner's measurements, Sam stood apparently twenty-six feet from J.E. when he fired the shot. Over Sam's objection, the trial court allowed the prosecutor to state this distance. The court cautioned the jury, however, that the prosecutor's statement was argument, not evidence, and that the jury should disregard it unless it was capable of confirming the distance by its own calculations.
Sam maintains, as he did below, that the disputed measurement is a fact as to which no evidence was presented and which the prosecutor should consequently have been barred from mentioning in argument. In presenting closing arguments to the jury, however, counsel are free to discuss not only the facts actually in evidence, but also any facts "within the range of reasonable inference which could be drawn from the evidence." Dorman v. State, 622 P.2d 448, 461 (Alaska 1981). The issue in this case is thus whether the disputed distance amounts to the type of factual inference that could properly be drawn from the facts in evidence, specifically, the two subsidiary measurements as to which Tanner testified. In our view, it is.
The formula for calculating the hypotenuse of a right triangle, commonly known as the Pythagorean theorem, is hardly an exotic equation that requires advanced training or experience to know and use. It is a basic mathematical formula involving skills that are at most one step removed from common multiplication and division; it is widely known and readily applied by those who know it. Routinely taught (and occasionally learned) in high school geometry courses across the country, the formula falls well within the realm of knowledge and experience that is common to many ordinary people. In complexity, its use may be likened to calculating the area of a rectangle or the circumference of a circle.
Certainly, the formula is not known by all of those who serve as jurors. But it would hardly be surprising to find one or more jurors in any given case who had the knowledge and ability to apply it. Nor could it plausibly be argued that jurors familiar with the formula would act improperly in relying on their knowledge during deliberations.
Sam does not dispute the accuracy of the measurement that was communicated to the jury. Moreover, the court instructed the jury to disregard the prosecutor's statement of the measurement if the jury was not itself familiar with the principles of geometry upon which the statement was based. While the line dividing common knowledge from scientific expertise may be difficult to discern and fairly debatable in many cases, it was not transgressed here.
Restriction of Sam's Final Argument
Sam additionally contends that the trial court improperly restricted his final argument. During the morning of the shooting, Sam made various statements to troopers and village police officers in Akiachak. The only recorded statement, however, was the formal interview conducted by Trooper Tanner, during which Sam evidently made a number of exculpatory statements. The state did not offer the recording to the jury.
On cross-examination of Trooper Tanner, Sam's counsel established that Tanner had recorded his interview with Sam and that this was the only interview recorded by the troopers. After having Tanner identify for the jury the tape on which the interview was recorded, Sam's counsel requested that the entire recording be played. Counsel made this request in the presence of the jury, openly stating that he thought the jury should hear it: "... I'd like right now to publish [the recorded interview] and play it for the jury. Move that it be admitted into evidence. I think the jury has a right to hear it." The prosecution objected.
In the ensuing anteroom conference, the trial judge pointed out that the recordings of Sam's exculpatory statements were inadmissible hearsay. See State v. Agoney, 608 P.2d 762, 764 (Alaska 1980); Stumpf v. State, 749 P.2d 880, 899 (Alaska App. 1988). The judge admonished Sam's counsel for raising the issue before the jury, noting that the court had previously made it clear that the tape would likely be inadmissible. The judge then explained to the jury that the tape would not be admitted, that the court had twice ruled it inadmissible, that the jury should not speculate about the contents of the tape, and that it should not think that evidence of value was being hidden.
At a later point in the cross-examination of Tanner, the court again admonished Sam's counsel for pursuing a line of questioning that appeared calculated to suggest that Sam had made (and that Tanner had recorded) exculpatory statements.
During closing argument to the jury, Sam's counsel was permitted to comment at length on the state's failure to gather available evidence and on its failure to present available witnesses. Counsel then called the jury's attention to a portion of Tanner's cross-examination in which Tanner was questioned as to whether he had ever specifically asked Sam if Sam had shot J.E. with the shotgun; Tanner answered that he had not asked Sam that specific question, but had come "pretty close."
After describing this portion of Tanner's testimony, Sam's counsel commented as follows to the jury: "How close was it? It was audio taped. You should hear how close it was." Upon objection by the state, the trial judge stated that the argument was improper and that it violated the court's order regarding admissibility of the tape. The court instructed the jury to disregard the comment.
Defense counsel resumed his argument. After telling the jury the court would instruct it that a reasonable doubt could arise from a lack of evidence, counsel said, "I am going to be talking about what was not given to you by the state, the lack of evidence." A short time later, in the midst of covering evidence that the state had not presented, counsel began what the court and the prosecution construed to be another reference to the state's failure to produce the recorded statements that Sam had given to Tanner. Sam's counsel told the jury that it had heard: "No other statements from Mr. Sam. Trooper Tanner...."
At this point the prosecutor cut Sam's counsel off with another objection. Another anteroom conference ensued, in the course of which the trial judge expressed frustration over counsel's deliberate disregard for the court's prior rulings. Sam's counsel did not deny that he had meant to refer to the state's failure to play Sam's recorded statement; to the contrary, counsel insisted that he should be allowed to argue the state's failure to play the recording as an indication that the state had failed to meet its burden of proof. Although emphasizing that counsel was free to argue the state's failure to produce available evidence that would have been admissible, the trial judge reiterated that counsel was forbidden from commenting on evidence that the court had found inadmissible. The judge went on to threaten a mistrial and sanctions if counsel "even approach[ed] it" again.
The trial judge further found that, by that point, there had been three occasions on which Sam's counsel had intentionally called the jury's attention to the fact that it had not heard the tape recorded statement. In the court's view, the potential prejudice stemming from these references warranted a cautionary instruction.[3] Accordingly, when proceedings before the jury resumed, the judge gave the following instruction:
Defendant's counsel may not lead you to believe that explanations were given by Mr. Sam that were consistent with his innocence but have not been presented to you or [are] being hidden from you by the State. Mr. Sam has no duty whatever to present any evidence and the fact that he has not done so may not be considered by you for any purpose. There are, however, ways for such evidence, if it exists, to be presented to you by the defense if it wished that these explanations be put before you.
Sam now claims that the trial court unduly restricted his ability to argue his case to the jury. Sam does not challenge the court's ruling that his tape-recorded interview with Tanner was inadmissible hearsay. Instead, he renews his claim that he should have been allowed to argue that the state's refusal to consent to the admission of this evidence amounted to a failure of proof on its part.
We find this argument frivolous. Carried to its logical conclusion the position Sam advocates would penalize the state for relying on the rules of evidence in virtually any situation involving exclusion of defense evidence, and it would subvert virtually any effort by the trial court to enforce the rules of evidence in such instances.
Sam also maintains that the curative instruction given by the court amounted to an impermissible comment on his right to silence. See, e.g., Baxter v. Palmigiano, 425 U.S. 308, 319, 96 S.Ct. 1551, 1558, 47 L.Ed.2d 810 (1976); Gunnerud v. State, 611 P.2d 69, 75 (Alaska 1980). However, Sam did not raise this objection below.
Given the circumstances described above, the trial court could reasonably conclude that significant prejudice had resulted from the repeated and apparently deliberate efforts by Sam's counsel to insinuate that the state was concealing potentially exculpatory statements that Sam had made to the troopers. The court could also reasonably conclude that the only effective way to cure this prejudice and eliminate unwarranted speculation would be to make clear to the jury not only that Sam's recorded statements had been ruled inadmissible and were not being concealed by the state, but also that Sam had the ability to present this evidence himself, if he so desired. The possibility that the challenged instruction might be read as suggesting that Sam had a duty to testify or present evidence seems minimal, at worst.
In summary, the challenged instruction was an appropriate response to the unusual problem created by defense counsel's insistent pursuit of a line of argument that the court had expressly precluded. Cf. Hilburn v. State, 765 P.2d 1382, 1390 (Alaska App. 1988) (it was proper to allow prosecutor to rebut inference that Hilburn could not have given more accurate explanation if he had taken the stand). We find no error.
Excessiveness of Sentence
Sam lastly challenges his sentence as excessive. Attempted first-degree murder is an unclassified felony, punishable by a minimum term of five years and by a maximum term of ninety-nine years. AS 12.55.125(b). Sam received a sentence of forty-five years with fifteen years suspended. At the time of sentencing, Sam was twenty-seven years old. Sam had a significant record of prior convictions, which included a misdemeanor assault. More notably, shortly before committing his current offense, Sam had been released from custody to await sentencing for assault in the third degree, a class C felony. The third-degree assault involved an unprovoked and unexplained attack in which Sam swung an ax at another person's head.
Citing Atkinson v. State, 699 P.2d 881, 885 n. 4 (Alaska App. 1985), Sam argues that he should have received a relatively lenient sentence because his conduct in the present case did not cause particularly severe injuries to his victim. In response, the state takes issue with Sam's effort to minimize the severity of J.E.'s injuries. The record supports the state's claim that J.E. suffered significant and apparently lasting harm as a result of Sam's crime. Moreover, even though greater harm might occur in some cases of attempted murder, this factor is only one of many that should properly be considered in determining an appropriate sentence.
Sam also analogizes attempted murder to the crime of second-degree murder, for which an identical sentencing range is prescribed. Compare AS 11.41.100, 11.31.100 with AS 11.41.110. Sam points out that this court has established a benchmark sentencing range of twenty to thirty years for second-degree murder cases. See Page v. State, 657 P.2d 850, 855 (Alaska App. 1983). Sam argues that his sentence should be held excessive because it violates the Page benchmark.
This argument is simply incorrect. The unsuspended portion of Sam's sentence thirty years falls within the Page benchmark range. Furthermore, the Page benchmark is meant to reflect the appropriate starting point for sentencing in second-degree murder cases involving first felony offenders. When he committed the current offense, Sam had already committed another felony assault, for which he was awaiting sentencing. Although the prior assault would not have formally qualified as a prior felony conviction for presumptive sentencing purposes because Sam had not yet been sentenced for it, Sam was a first felony offender only in the most technical sense.
Finally, Sam's argument that he deserved a lenient sentence disregards the unprovoked and seemingly inexplicable nature of his life-threatening conduct. We have previously recognized that incidents of unexplained and unprovoked violence may indicate that an offender is seriously disturbed and unusually dangerous. For this reason such conduct may justify the imposition of an exceptionally severe sentence, even for a first offender. See, e.g., Bolhouse v. State, 687 P.2d 1166, 1176, 1179 (Alaska App. 1984) (Bryner, C.J., concurring); Faulkenberry v. State, 649 P.2d 951, 955-57 (Alaska App. 1982). Given Sam's commission of two seemingly incomprehensible, life-threatening assaults within a short span of time, the sentencing court could properly find him to be an unusually dangerous offender.
Having independently reviewed the entire sentencing record, we conclude that the sentence imposed below is not clearly mistaken. McClain v. State, 519 P.2d 811, 813-14 (Alaska 1974).
The conviction and sentence are AFFIRMED.
NOTES
[1] We note that federal courts have not hesitated to apply the rationale of Luce v. United States outside the context of cases involving impeachment by prior conviction. See, e.g., United States v. Gwaltney, 790 F.2d 1378, 1386 (9th Cir.1986) (tactical reason found for not calling character witness at trial after judge ruled that certain rebuttal evidence would be allowed); United States v. Donlon, 909 F.2d 650, 656 (1st Cir.1990) (trial court refused to limit cross-examination in advance of witness taking stand; reviewing court found defendant who did not take stand could not appeal ruling); United States v. Nivica, 887 F.2d 1110, 1115-17 (1st Cir.1989) (defendant could not appeal ruling in favor of government impeaching witnesses without having actually called witness and objected to specific questions during testimony).
[2] The Pythagorean theorem holds that the square of the length of the hypotenuse of a right triangle equals the sum of the squares of the lengths of the other two sides. Webster's New Collegiate Dictionary, 961 (9th ed. 1983). The theorem is commonly expressed by the formula: a[2] + b[2] = c[2].
[3] The judge summed up his view of the problem as follows:
[Defense counsel], you're placing the court into a position where it has to comment upon [Sam's] silence. How else can the court explain to the jury that there's a reason those things can't be said and the only way they can be said is by [Sam] saying them and he chooses not to?
....
They chose their evidence ... what you're saying, [defense counsel], is that because they introduce admissions against interest, clearly admissible, you can comment that they didn't include what is not excluded as hearsay, in other words, exculpatory, and that just rips asunder the foundations of evidence in a criminal trial, that you can't hide behind that shield. You can't say he said good things and they're not telling you.