Beauty and the sharp fangs of the beast: degree of angularity predicts perceived preference and threat

The evaluation of angular vs. curved forms has a long history in psychology but few of the many studies conducted have examined actual degree of angularity. In two experiments, we present observers with randomly positioned and randomly oriented texture displays of angles viewed within a circular frame. The angle conditions varied from 0° to 180° in 20° increments, covering the entire spectrum of possibilities including acute, obtuse, right, and straight line angles. In Experiment 1, 25 undergraduates rated the perceived beauty of these displays. In Experiment 2, the same stimulus set and procedure were used with 27 participants instead judging perceived threat. Based on the findings in the literature, we predicted that sharper angles would be judged less beautiful and more threatening. The results were mostly confirmed. Acute angles are preferred less but there are also distinct preferences for right angles and straight lines, perhaps due to their greater familiarity in constructed environments. There was a consistent and anticipated finding for threat in the second study: the sharper an angle, the greater its perceived threat. Fear of sharp objects as assessed in a personality questionnaire was found to positively correlate with threat judgements. Future work should look more closely at degree of angularity in embedded object contours and at individual response differences.

The study of angularity in esthetics dates back more than a century with a number of early studies showing that angled lines are associated with negative emotions such as agitating, hard, and furious. On the other hand, curved objects have been associated with more pleasant feelings like quiet, merry, and gentle (Hevner, 1935;Lundholm, 1921;Poffenberger & Barrows, 1924). Bar and Neta (2006) more recently demonstrated a greater liking for curved as opposed to jagged shapes. They had participants judge real objects and meaningless patterns in a forced-choice like/dislike procedure and found a consistent preference for shapes with curved as opposed to sharp contours. They proposed that sharp objects trigger a sense of threat while rounded features convey a sense of warmth. In a subsequent study, they found greater activation of the amygdala (involved in processing fear and arousal) in response to sharp-angled contours compared to rounded counterparts. They hypothesized that such low-level contour features might be sufficient to trigger a fast evaluative response used in determining the presence of danger (Bar & Neta, 2007). Silvia and Barona (2009) later replicated this finding controlling for other preference factors like symmetry, prototypicality, and balance using as their stimuli circles, hexagons, and curved and angular polygons. Damiano et al. (2021) found that images with angular contours in an affective picture set were rated as negative while those with long contours were rated as positive. For abstract line drawings, smooth, long, horizontal contour scenes were considered to be positive and safe, while short angular contour scenes were judged as negative and threatening. Leder et al. (2011) examined whether the emotional valence of the objects themselves modulates this so-called "curvature effect". They found the curved over jagged preference for objects with neutral and positive emotional valence only, but not for objects with negative valence like "bomb" or "snake". This suggests that higher-level semantic properties can over-ride lower-level contour features in determining preference for such objects. Further evidence for this comes from a study by Corradi et al. (2018). They found no difference between real and meaningless objects at brief presentations, implying that the decision for these conditions was based on contours only. However, at longer presentation times, the pattern of results diverged implying the influence of semantic or conceptual factors related specifically to meaningful objects.
Another stimulus property that influences this effect is the number of lines present in a pattern. If the number of total contours is relatively small, the difference between curved and angular shapes is found to be a good predictor for esthetic judgements of pleasing and harmonious (Stanischewski et al., 2020). But when the pattern contains a large number of lines, edge-orientation entropy (roughly, the number of lines at different orientations) is a better predictor. The results were interpreted as the result of separate evaluative processes for objects that have fewer contours, as opposed to textures which have more. Degree of curvature also makes a difference. Hubner and Ufken (2022) found that lines of intermediate curvature were most associated with beauty, those corresponding to version 4 (and 5) of Hogarth's 'Line of Beauty'.
Individual subject variables and experience have also been found to influence the angularity effect. As such, these correspond to "internal" personality factors as opposed to "external" stimulus-based factors. Silvia and Barona (2009) obtained an effect of artistic expertise. In this study, angularity reduced preference at lower levels of expertise but as expertise increased, the effect of angularity decreased. Cotter et al. (2017) found that people with higher levels of openness to experience were more sensitive to the effect of contour when evaluating the pleasantness of abstract unfamiliar shapes. Further, Vartanian et al. (2017) showed that non-expert judges indicated they would be more likely to enter a curvilinear rather than rectilinear architectural space. They also found greater contour sensitivity for beauty judgements among experts.
Preference for curved features has been shown in other areas as well including product design, architecture, and paintings. Based on self-report measures, study participants are more likely to buy consumer products when packaged using round as opposed to jagged designs (Westerman et al., 2012). Architectural spaces are also judged more beautiful when they contain curvilinear as opposed to rectilinear design, with curvilinearity found to activate the anterior cingulate cortex (Vartanian et al., 2013). Participants also assign higher ratings to curved compared to sharp-angled versions of abstract novel paintings and want curved versions more when asked if they want to take the paintings home.
How can we best explain this phenomenon? Palumbo et al. (2015) found that the difference between angular and curved objects may lie not so much in threat assessment but in the fact that curvature is considered more pleasant than angularity. In one of their experiments, they found no difference in approach/avoidance reactions to curved and angular polygons even in a case where the angles were more pronounced. This difference would not have been obtained if the angular objects were considered more threatening. However, their participants were faster and more accurate moving manikins toward curved shapes, in concordance with the interpretation that they were more pleasant. In a separate experiment, they found that angular polygons were associated with danger, negative concepts and male names, while curved polygons were associated with safety, positive concepts, and female names.
Interestingly, the angular-curvature difference has also been found in nonhuman great apes (adult chimpanzees and western lowland gorillas) as demonstrated in a two-alternative forced-choice paradigm, albeit with different forms of behavioral expression (Munar et al., 2015). Using this same paradigm, it was also discovered that curvature is preferred over angularity when tested cross-culturally. Preference results are consistent across human samples tested in Spain, Mexico, and Ghana (Gomez-Puerto et al., 2017). These studies reinforce the idea that a threat response to angularity is universal and hard wired rather than acquired through experience, although it may be modulated by other factors.
In most of the research previously reviewed, angular patterns were compared against rounded versions. However, rarely was the degree of angularity ever assessed. This is curious since it is quite easy to make an object look more or less sharp by simply varying the degree of an angle. Simply put, smaller angles appear sharper and larger-valued angles less so. The purpose of this study is to therefore measure the effect of aesthetic and threat responses to the entire range of angularity. If smaller angles appear sharper, we would expect them to also appear more threatening. Also, since positive affect is associated with curvature and negative affect with angularity, we would expect lowered aesthetic ratings for sharper angles.
In both of the following experiments, we use the same stimulus set. This is a collection of angles presented at random orientations and locations within a circular field. We use the entire continuum of possible angles. This includes acute angles which are those greater than zero but less than 90°, as well as obtuse angles which are greater than 90° but less than 180°. For comparison, we also include right angles equal to 90° and straight angles (lines) equal to 180°. These last two examples may be responded to differently since they are highly familiar, being found everywhere in human-engineered environments. For example, most corners of objects like furniture, walls, and doors are 90°, while the edge of manufactured objects and surfaces tend to be straight.
If sharper angles elicit more threat and negative affect, they ought to induce lowered ratings of perceived beauty as well. If this were the case, we would expect ratings of beauty to be lower for acute and higher for obtuse angles. Furthermore, as degree of angle increases, we might find a monotonic increase in beauty ratings. The opposite pattern would be expected for threat judgements. Here, estimates of perceived threat would be highest at smaller angles and hypothesized to drop monotonically as angle increases. The prediction for right angles and straight lines could conceivably differ from this pattern. Due to their familiarity, they might both be rated higher in beauty. However, a straight line could be perceived as sharp. If this were the case, beauty ratings for 180 angles would be lower and threat ratings for it higher.
In summary, we make the following four hypotheses: 1. Beauty ratings are expected to increase incrementally from 0° to 180° as the angles become less sharp. This is tested in Experiment 1. 2. Threat ratings are conversely expected to decrease incrementally from 0° to 180° as the angles become less sharp. This is tested in Experiment 2. 3. The cases of 90° and 180° are expected to be special due to their familiarity. Beauty ratings for these two conditions might be much higher. This will be evaluated in Experiment 1. 4. It is unclear what to predict for 90° and 180° for perceived threat. These two cases might not deviate from the overall trend. If straight lines are perceived as piercing, then threat assessments might increase for the 180° condition.

Participants
Twenty-five undergraduates participated to fulfill a class requirement. There were 13 men and 12 women. Vision was normal or corrected-to-normal. Average age of the students was 19.6 years. All participants voluntarily agreed to participate and signed a consent form. The study was previously approved by the Manhattan College Institutional Review Board. American Psychological Association ethical standards and data confidentiality were followed. The data have been made available on the Open Science Framework.

Stimuli
We employed ten different angle conditions dividing the interval between 0° and 180° by 20° intervals. This resulted in 20°, 40°, 60°, 80°, 100°, 120°, 140°, 160°, and 180°. A 90° condition was also included because of its frequency of occurrence in human-synthesized environments. To reduce any frame of reference effects, the angles were presented inside of a circular aperture. Thirty-three angles were placed inside of this space. This number was determined a priori because it filled the area within the circle without being either too dense or sparse. Each individual angle was created by a straight line with one end anchored at the center of an invisible circle equal to its radius. The second arm of the angle was an additional line of equal length that was then "swept" around the circle by the specified degree. In this sense, each line of the angle could be conceptualized as two equal-length arms of a clock. The orientation of each angle was then assigned a random value between 0° and 360°.
The position of each angle was randomly assigned as follows. The enclosing circular frame was centered inside of an invisible square whose sides were divided into 100 equal units. An x-and y-coordinate were separately randomly generated and the center of the angle was placed at this location. If the angle fell outside of the circle or the arms of the angle touched the circle, a new coordinate pair was generated. A minimum inter-element spacing equal to one half of the angle radius was enforced. If any two angles came closer than this distance, a new position was generated. Figure 1 shows examples.
The diameter of the global circular frame was 24 cm. The diameter of the local invisible circles determining the angles was 2.3 cm, making the scale of the display elements relative to the frame approximately 10:1. The angles and frame were black and made at a two-point line thickness to increase their visibility. Each pattern was presented on a white background. The center of the circular frame was at the center of the computer screen and viewed at an average distance of 60 cm.

Procedure
Eight different versions were created for each angle condition yielding a total of eighty unique stimuli. These constituted a single block of trials. Trials were randomized within blocks. Participants viewed three blocks in an experimental session (10 × 8 × 3 = 240 total trials) which took on average of about 15 min to complete. Participants were given as much time as they needed to respond.
Rating scale judgments were obtained for each trial. Beauty judgments were made using the number scale that ran across the top of the computer keyboard. This scale ran from 1 to 7, with "1" labeled as A Little Beautiful, "4" labeled as Average Beauty, and "7" labeled as Most Beautiful. Participants were instructed to use any number from the entire scale. They were told there was no right or wrong answer and that they could rate the patterns in any way they wanted. This was done to reduce any experiment-induced judgment criteria or demand characteristics. If any number other than 1-7 was entered, the participant would not be able to advance to the next trial. If this occurred, they were instructed to re-enter an appropriate value.

Results and discussion
The data were first screened for outliers. Responses that took longer than 8.5 s were considered to be moments of inattention and removed prior to analysis. These constituted less than three percent of the tail end of the reaction time distribution. In addition, two participants were dropped from the analysis because they did not follow instructions.
A one-way analysis of variance (ANOVA) was performed with effect sizes calculated as partial eta squared. There was a significant main effect of angle F(9, 220) = 12.83, p < 0.01, η p 2 = 0.34. Power for this alpha, sample size, and effect size for a post hoc fixed effects omnibus, one-way F test was 0.97. Figure 2 shows the line plot of this interaction. Judgements were lowest for the 20° condition, steadily increasing up to and peaking at 90°. After 90°, there was a decrease in beauty ratings but a sharp rise for 180°. A Tukey HSD least square means analysis was performed to see which conditions differed statistically from one another (Q = 3.16, alpha = 0.05). These results are shown in Table 1. As can be seen, the right angle was liked the most with a high preference also for the straight line 180° condition. Deviations from 90° show a decline in ratings. Generally speaking, the more acute or the more obtuse the angle, the less they were preferred.
The results show partial support for the threat hypothesis. The sharpest angle, 20°, was preferred the least. As sharpness decreased with larger angles toward the 90° condition, there was a corresponding increase in beauty ratings. The peak at 90° supports the familiarity hypothesis, suggesting that perpendicular angles are preferred because we see them repeatedly in synthetic and architectural scenes. However, we did not find a further increase in ratings past 90°. The effect for obtuse angles shows just the opposite: a decline in ratings for angles greater than 90° but less than 180°. The increase we see on either side of 90° instead supports the idea that 90 degree angles may be aesthetically canonical. By this, we mean that they are preferred under most circumstances and that any deviation away from them produces lowered beauty estimates.
Participants showed a clear preference for the 180° degree condition, equivalent to a straight line. This result is somewhat unexpected. A straight line, even though it lacks angularity, can be perceived as sharp. For example, straight lines of the length presented here could be perceived as needles which are sharp and therefore threatening. Instead, these lines were among the most liked of all the conditions shown. Straight lines are also ubiquitous in human-made environments, forming the sides of  many objects. In fact, straight lines typically form the edges or contours of constructed objects, while 90° angles usually form the corners. So, familiarity may explain why both of these conditions were liked so much. It should also be mentioned that we included 180° as a control. It is not an angle and in fact may be judged in an entirely different way than angles, since angles are spatially two-dimensional and straight lines are one-dimensional.

Experiment 2
The first experiment showed that sharpness can reduce perceived beauty for certain angles. However, it did not provide any linkage between degree of angularity and perceived threat. Just because objects look increasingly sharp does not mean they appear more threatening. To test this directly, we performed a second study in which participants rated angles in terms of perceived threat.
In addition, we collected ratings for several personality measures to see if these might predict perceived threat. These measures varied in how closely associated they were to the angular stimuli. For example, asking participants about their fear of sharp objects is very closely related to the implied visual appearance of the angles. Asking participants about their fear of getting cut or bruised is slightly less associated with this attribute. Asking them about how anxious or emotionally sensitive they are is even less associated. We expect that stronger levels of association for these questions will produce stronger correlations with perceived threat.

Participants
Twenty-seven undergraduates participated to fulfill a class requirement. There were 7 men and 20 women. No student that participated in the first study was allowed to participate in the second, so they would remain naive regarding its nature and aims. Vision was normal or corrected-to-normal. Average age of the students was 19.4 years. All participants voluntarily agreed to participate and signed a consent form that was approved by the Manhattan College ethics board. Because some of the questions might have been mildly distressing, we included wording to indicate they could skip such questions or withdraw from the experiment at any time. A Manhattan College Institutional Review Board Application for Amendment (Form C) was filed to accommodate these changes and approved (Approval Code F21-01). Psychological Association standards and data confidentiality were followed. The data have been made available on the Open Science Framework.

Stimuli
The same angular conditions from the first study were used. Size, configuration, and location of each pattern were identical. A participant information form was designed to assess the degree of perceived threat from the angular stimuli and was administered after the experiment was completed. This consisted of the following set of questions: How scared are you of sharp objects? (1 = Not scared at all, 7 = Very scared) Do you have a fear of getting cut? (1 = Not fearful at all, 7 = Very fearful) Do you get injured or bruised easily? (1 = Not easily, 7 = Very easily) Do you enjoy watching scary movies? (1 = Not at all, 7 = Very much) Do you like to take risks? (1 = Very risk averse, 7 = Very risk-taking) How anxious or fearful are you? (1 = Not anxious at all, 7 = Very anxious) Are you an emotionally sensitive person? (1 = Not at all, 7 = Very sensitive) Some of these questions are of a personal nature and may have been mildly upsetting or distressing to the participants. This was therefore announced on the first page of the consent form. The subjects were told that they could quit at any time or skip questions that they found too upsetting. They were reminded that all the information gathered was to be held in strict confidentiality and that at no time were individual names to be used in the reporting or publishing of the results.

Procedure
Number of trials, blocks, and presentation conditions were the same as in Experiment 1. Instead of rating beauty, participants rated perceived threat. They were provided with the following description to make a response. If you think the pattern is Very Threatening, then enter a seven (7). If you think the pattern is only A Little Threatening, then enter a one (1). If you think that the pattern is just of an Average Threat, then enter a four (4). To ensure that participants understood the response, a standard written definition of threat was on the desk adjacent to the computer for them to consult. This was as follows: A threat is something that appears dangerous and can inflict pain or cause potential harm.

Results and discussion
Four participants were removed from subsequent analyses for failing to follow directions. The reaction time distribution for the threat variable was examined and all responses greater than 4.5 s were removed prior to analysis because they were considered moments of inattention. This amounted to less than one percent of the total data. Responses to the seven personality questions were not timed and all of the data for these rating scales were retained. The shape of the distributions for the personality questions was normal or approximately normal and the full range of the scales was used.
A one-way analysis of variance (ANOVA) was performed. There was a significant main effect of angle F(9, 220) = 161.51, p < 0.01, η p 2 = 0.86. Power for this alpha, sample size and effect size for a post hoc fixed effects omnibus, one-way F test was 1.00. As can be seen in Fig. 3, there was a clear-cut effect for perceived threat. The sharper the angle, the greater the perceived threat. In general, average threat decreased with an increase in angle, although there is a plateau in the middle, centering at 90°. There was also a more noticeable drop-off in this downward trend for the 180° condition. The plateau in the bar plot shows that the 90° angle and those adjacent to it were perceived less threatening. The drop-off at the end shows that the 180° condition was also seen as least threatening. Again, both of these effects may be due to the increased familiarity of right angles and straight lines. Table 2 shows the means and standard errors along with the differences based on a Tukey least square means test (Q = 3.16, alpha = 0.05). Looking at the statistically significant differences between means, we can confirm that 20°, 40°, and 60° differ from each other and that 100°, 120°, 140°, 160°, and 180° also all differ from each other. In contrast, 60°, 90°, 80°, and 100° do not differ statistically. This confirms the existence of a leveling-off effect in the middle of the downward trend centered around the right angle.
We next correlated personality ratings with perceived threat. The mean rating for each participant was correlated with their mean rating of perceived threat across all angles for each questionnaire item. Only one of the seven variables was statistically significant. Participants with a greater fear of sharp objects rated the angular patterns more threatening r(21) = 0.50, p = 0.018. The upper 95% confidence interval for this correlation is 0.723 with a lower 95% confidence interval of − 0.010. The scatterplot for this effect is shown in Fig. 4. This question had the highest degree of association with the pattern's perceptual attributes. It was asking directly about sharp objects whereas the other questions were more remotely associated and related to skin sensitivity, anxiety, and emotionality.

General discussion
In Experiment 1, we presented angles at regular intervals to participants and asked them to judge their perceived beauty. We hypothesized that sharper angles would be perceived as more threatening and that this would induce a negative affective state, lowering beauty ratings. The strict version of this prediction would have ratings lowest for the smallest angles and increasing steadily as the angles become less acute, then more obtuse until they formed a straight line. This prediction was partially confirmed. There was an increase in ratings across the acute continuum, with the function peaking at 90°, then steadily decreasing thereafter. Ratings for 180° were higher than what we expected, indicating it was either not perceived as sharp or processed differently because it was not an angle.
The shape of the beauty function peaks at 90° with an asymmetric fall-off to either side. This suggests that 90° and 180° may be "canonical angles", perceived as most beautiful and with any angles deviating away from them being perceived as diminishingly less attractive. If this were the case, the effect for acute and obtuse angles may not be due to perceived threat but instead to their proximity to these two salient stimuli.
One explanation for this is that perpendicular angles and straight lines are commonplace in constructed environments. It is well-known that familiar objects are preferred and that this can be created through repeated exposure or processing fluency (Reber et al., 2004). If this were the mechanism behind our results, then it would be interesting to test participants from remote areas who have not had much experience with such angles, as has been done in the classic study on the Muller-Lyer illusion (Deregowski, 1989;Segall et al., 1966). These studies showed cultural differences in the ability to perceive the illusion based on one's exposure to "carpentered worlds". Europeans and Americans who see many straight and perpendicular lines were more likely to experience the illusion while Kalahari hunter-gatherers who seldom see these lines were least susceptible.
In Experiment 2, we used the identical stimulus set and procedure varying only the type of judgement. Participants in this study were asked to rate the perceived threat of the patterns. Based on the findings in the literature, we predicted that acute angles would be judged more threatening than obtuse. More specifically, we expected to find threat to be a monotonic decreasing function of angle. This was in fact the case, with most adjacent angles being statistically different from each other across the spectrum. The exception was for angles adjacent to 90° where there was a slight plateau. This rise in perceived threat is small but it interrupts the consistent downward trend. The lowest perceived threat is for 180°, so it seems that this straight line was evidently not perceived as a needle or other sort of puncturing object.
Personality questions were obtained from our participants in this experiment. We thought that individuals who were more scared of sharp objects, had a fear of being cut or bruised, or who were more anxious, fearful or emotionally sensitive might show an exaggerated angularity effect. Conversely, we suspected that those who enjoyed scary movies or taking risks might show a more attenuated effect. To this end, we correlated these measures with their ratings. The only question that correlated significantly with threat was a fear of sharp objects, probably due to its specificity with regards to the task. It may be that some of the personality questions we used due to their sensitive nature were not answered truthfully or did not accurately assess internal states. If so, a more extensive test ought to be used, one that is more validated and reliable.
To better assess the relationship between perceived threat and beauty, a within-subjects design could be employed where the same individuals rate angles for both measures. Then a direct correlation between the two variables could be made. However, based on our two experiments with different sets of subjects, it seems unlikely that there would be the predicted inverse relationship. The data of Experiment 1 would need to be decreasing continuously across the span of values to obtain this result. It is possible that perceived threat affected beauty ratings for acute angles only, because it is in this delimited range that we see rising and falling functions for beauty and threat, respectively.
It should be noted that the overall speed of threat judgments was much faster than that of beauty judgments. The cut-off point for inattentive responses marking outliers was 8.5 s in Experiment 1 but only half of this, 4.5 s in Experiment 2. The mean response time for beauty judgments was over 2 s (M = 2.10, SD = 18.74), while for threat, it was about 1.5 s (M = 1.45, SD = 11.70). In addition, the RT distribution was more positively skewed in Experiment 1 (Skp = 1.73) than in Experiment 2 (Skp = 1.03). These faster responses correspond to the idea that perceived threat to sharp objects is an automatic and perhaps pre-attentive reaction. Aesthetic evaluation of sharpness may instead be of a longer more secondary nature. This interpretation conforms with that provided by Bar and Neta (2007) and with the results of other studies previously reported (Corradi et al., 2018;Leder et al., 2011).
This study did not examine curvature at all. Our main concern here was with angularity and how variations in angle would affect perception. Future work could examine curved versions of these stimuli by substituting curves for lines, resulting in "soft" angles. This might ameliorate the effect or perhaps eliminate it altogether. Also, we deliberately used texture patterns to avoid any semantic associations, but it would be interesting to look at degree of angularity as embedded contours in closed figures. One could make random polygons that more closely resemble objects to see if the effect still holds. These polygons could then be compared to meaningful real-world objects whose contours were manipulated in the same way. As we saw earlier in the introduction, there may be separate processing strategies for objects and textures (Stanischewski et al., 2020).
Finally, we mentioned that familiarity may explain the different reaction to 90 and 180 stimuli. In addition to looking at cross-cultural differences, there are a number of other experiential or personality variables that are relevant here.
Art expertise could be looked at, as could the Big-Five traits. Individuals high in art expertise showed decreased effects of angularity compared to a control group (Silvia & Barona, 2009). Perhaps this is because art experts have more experience viewing non-canonical angles in abstract artwork. Remember also that non-architectural experts were more likely to enter a curvilinear space, suggesting increased familiarity with rectilinear shapes or less automatic association of comfort with curves among architects .